The HS2 high-speed rail project has an estimated £3.3 billion funding gap which the Government has yet to decide how to fill, a report from a Whitehall spending watchdog said.

It was not clear how HS2 - which runs through Tory heartlands and is bitterly opposed by some - would deliver and rebalance economic growth, the report by the National Audit Office (NAO) added.

The timetable for planning phase one of the project - from London to Birmingham with work due to start in 2016/17 - was "challenging", the NAO said.

This challenging timetable "makes delivering this work difficult and increases the risk that the programme will have a weak foundation for securing and demonstrating success in the future", the report said.

Expressing "reservations" about the business case for HS2, the NAO said the Department for Transport's (DfT) methodology for appraising the project put a high emphasis on journey-time savings, from faster and more reliable journeys.

But the report added that the relationship between these savings and the strategic reasons for doing the project, such as rebalancing regional economies, was unclear.

The NAO said it was also unclear whether the business case covered just phase one or the full route including phase two - the Y-shaped network from Birmingham to Manchester and Leeds due to open in 2032/33.

The report said phase two had a strong economic case but that this was much less certain as route designs were less well-developed.

Saying there were "risks to affordablity", the NAO went on: "The NAO estimates that there is a £3.3 billion funding gap over four years (2017-18 to 2020-21) which the government has yet to decide how to fill."

The report said this "gap in affordability" coincided with the "peak spending years for phase one".

The NAO went on: "The department capital forecast for these four years is £33.7 billion but its capital budget if kept constant at 2014-15 levels would be only £30.4 billion."

The NAO said the benefit-cost ratio - the cost of the project set against the likely benefits it will bring - had twice contained errors and that the current estimate of £1.4 in benefit to every £1.0 spent was "likely to change".

It added that between March 2010 and February 2011 benefits from HS2 reduced by £12 billion, with nearly two-thirds of this reduction due to errors in the way passenger demand was modelled.

The report said that the DfT estimated the line would support 100,000 jobs through development around stations in constructing and operating the line.

The report went on: "It (the DfT) does not know how many jobs would be created without this investment."

The NAO also said that HS2 Ltd had not yet analysed the effect of premium pricing on forecast passenger demand, revenues and the benefit-cost ratio.

The report went on: "To forecast passenger demand, HS2 Ltd uses the same average fares for high-speed and conventional rail in its models, although premium fares are charged for HS1 (the London to Folkestone Channel Tunnel link)".

NAO head Amyas Morse said: "It's too early in the HS2 programme to conclude on the likelihood of its achieving value for money.

"Our concern at this point is the lack of clarity around the department's (DfT) objectives."

He went on: "The strategic case for the network should be better developed at this stage of the programme.

"It is intended to demonstrate the need for the line but so far presents limited evidence on forecast passenger demand and expected capacity shortages on existing lines.

"It is also unclear how HS2 will transform regional economies by delivering jobs and growth."

"The department is trying against a challenging timetable to strengthen its evidence and analysis, which at present provide a weak foundation for securing and demonstrating success in the programme in future."

Commenting on the report, House of Commons Public Accounts Committee chairman Margaret Hodge said: "The DfT has produced a business case that is clearly not up to scratch and shows no signs of having learnt the lessons from HS1, which the committee reported on last year. "

She went on: "Some of their (the DfT's) assumptions are just ludicrous. To take just one example, on the benefits to business travellers, the department continues to assume that business travellers do not work when on the train and to use data that is over 10 years old.

"HS1 ended up costing the taxpayer billions when it was supposed to pay for itself. An estimated £3 billion funding gap has been identified for HS2, already bringing into question the affordability of this project."

Ms Hodge continued: "There is virtually no evidence in this business case to support claims that HS2 will deliver regional economic growth, one of the key aims and justifications for this project.

"We have been told that it will deliver around 100,000 new jobs but there is no evidence that all these jobs would not have been created anyway.

"The department has also set an extremely ambitious timetable for the project, with no room for mistakes. Past experience does not fill us with confidence in this optimism.

"Unless the department gets its act together, HS2 will not deliver all intended benefits for travellers and the regions, and it will not deliver value for the taxpayer.

A section of the HS2 high speed rail network could be tunnelled under a busy section of the M6 in a move to reduce disruption to the local area.

HS2 Ltd, which is responsible for developing the network, will recommend the line be tunnelled under the Bromford Viaduct which carries the M6 motorway between Castle Bromwich and Gravelley Hill.

The initial route would have seen the new line follow the existing Derby to Birmingham rail line before running for about 1km under the viaduct.

The plan would have involved a major remodelling of a busy junction between the A47 - Bromford Lane and Heartlands Parkway - and the re-alignment of part of Chester Road.

It would also have required moving the River Tame south, building flood defences and relocating power lines and pylons.

Local school playing fields and social clubs would also have been affected by the plans.

The revised option would see a reduction in land-take and leave more community facilities unaffected, HS2 Ltd said.

The revised option will be included in the draft Environmental Statement for the first phase of HS2, set to be published shortly and be subject to public consultation before any decision is made.

Alison Munro, HS2 Ltd chief executive, said: "Following a review of the alternatives a tunnel design was considered to be the preferred option as it proved to be less complex in engineering terms and would avoid the loss of local community facilities including the local schools' playing fields and social clubs including Bromford Residents' Club and Bromford Neighbourhood Office.

"Birmingham's position at the heart of Britain's new high speed rail network was set out in January with the publication of the preferred route for phase two.

"Along with significantly reduced journey times to Leeds, London, Manchester, Sheffield and the East Midlands, HS2 will free up much-needed capacity on existing lines.

"The region will also benefit from an expected 8,000 jobs created through the regeneration and development of the HS2 interchange at Birmingham Airport and Curzon Street stations, as well as opportunities from the 9,000 construction jobs on phase one."

Work on phase one of HS2, from London to Birmingham, is set to start in 2016/17 with services beginning in 2026.

Phase two, taking the line north in a Y-shape to Manchester via Crewe and to Leeds via Derby and Sheffield is set to be completed around 2032/33.

Transport Secretary Patrick McLoughlin said: "I welcome any examination of the HS2programme, but I do not accept the NAO's core conclusion.

"This is because it depends too much on out-of-date analysis and does not give due weight to the good progress that has been made since last year.

"This includes the appointment of an expert management team and the announcement of detailed plans for the line north of Birmingham."

He added: "The case for HS2 is clear. Without it the key rail routes connecting London, the Midlands and northern England will be overwhelmed.

"HS2 will provide the capacity needed in a way that will generate hundreds of thousands of jobs and billions of pounds worth of economic benefits.

"Economic modelling is just the start of the story. If we only relied on modelling we would not have built the M1, parts of the M25 or the (Tube's) Jubilee line extension to Canary Wharf.

"We are not building HS2 simply because the computer says 'yes'. We are building it because it is the right thing to do to make Britain a stronger and more prosperous place."

Hilary Wharf, director of HS2-opposing group HS2 Action Alliance, said: "NAO's report highlights the failings in the fundamentals of HS2's business case and is a scathing indictment of the bogus case the Government has constructed.

"HS2 simply cannot withstand independent scrutiny. The NAO join a long list of independent bodies and economists who find HS2's planning and business case woefully lacking."

She went on: "NAO catalogue numerous failings, from DfT's assumptions on valuing journey time savings - incredibly, half the claimed benefits depend on no-one working on trains - to finding no evidence HS2 rebalances the economy.

"It is astounding that the Government - rather than dropping HS2 and saving £36 billion of taxpayers' money - table an HS2 Preparation Bill to waste money even faster."

On the £3.3 billion gap in affordability, the DfT said: "We do not recognise the funding gap that the NAO quotes."

Commenting on the report, CBI business environment director Rhian Kelly said: "It is early days in a 20-year project but the Government needs to implement lessons quickly from previous (rail) franchising failures. Industry, investors and taxpayers must see a watertight business case and programme management.

"There is very little advantage in prolonging the timetable given the West Coast Main Line is set to reach full capacity by the mid-2020s - squeezing out passengers and freight. Ministers need to secure real consensus on the route now to avoid the project being hit by years of delays further down the line.

"HS2 cannot be built in isolation. We need sustained, additional capital investment in existing road and rail networks now to meet increased demand."

For Labour, shadow transport secretary Maria Eagle said the report was a "worrying wake-up call" for the Government.

"A new high-speed line between north and south is vital to tackle the rapidly advancing capacity crunch on Britain's railways, yet the NAO is damning about the Department for Transport's ability to deliver it," she said.

"It is deeply concerning that, just one week after the Queen's Speech, the NAO believes the Government's timetable for delivering the legislation necessary for HS2 is hopelessly unrealistic."

Stop HS2 campaign manager Joe Rukin said: "Just a couple of days after Patrick McLoughlin asked MPs to give him a blank cheque for HS2, the National Audit Office have produced a damning report into the project.

"The project is out of control because the politicians involved have been seduced by the words 'high speed rail' and have been complicit in fabricating a case for their vanity project."

"The NAO say everything the Stop HS2 campaign has been saying for three years. The Government and MPs haven't wanted to listen to us, but the surely have a duty to listen to the NAO."

Philip Atkins, leader of Staffordshire County Council, said: "The watchdog says it is unclear how HS2 will fulfill promises to transform economies and this is certainly the case in Staffordshire - as there are no economic benefits to the county. If the link is to be imposed on Staffordshire then there needs to be absolutely clarity on the scheme, the proposed route, mitigation and intended compensation arrangements for families."

Mr McLoughlin defended the plans, insisting they were necessary to help the UK compete in the "global race" against other economies.

He told the BBC Radio 4 Today programme: "As a Government you don't just plan for next year, you have to plan how we compete in that global race, how do we show businesses to come to this country because you have got the right sort of transport connections, that you have got the right kind of communications.

"Transport has gone up the political agenda incredibly over the last 20 years since I was last in the Department for Transport as a junior minister. We are looking to how Britain competes not just now but in that global race ahead of us."