Chancellor George Osborne has welcomed Sir David Higgins' recommendations for HS2, but warned there will be "no increases" in spending on the £50 billion poject.
Mr Osborne described the high-speed project as "essential to the future of this country".
However, he cautioned: "We must be conscious of the price, and there will be no increases to the overall spending envelope set for HS2 at the last spending review."
Earlier today, Shadow Transport Secretary Mary Creagh said there would be no "blank cheque" for the project.
Ms Creagh told BBC Radio 4's The World At One that Labour would be supporting the hybrid bill due to come before parliament but argued that the project had "suffered from mismanagement".
HS2 contingency savings cannot be guaranteed, the project's chairman has told ITV News' Deputy Political Editor Chris Ship:
Boss of #hs2 says he can't bank any savings in the £7.4bn contingency yet - cos the political/legislative delays & uncertainties too great
Plans to speed up the development of HS2 and extend it to the north more quickly have been backed by the government.
Asked whether the coalition would take action to accelerate the passage of the HS2 Bill through Parliament, Prime Minister David Cameron's official spokesman said: "We want it to proceed as quickly as it can, but it is obviously a very lengthy Bill."
Earlier today, Transport Secretary Patrick McLoughlin said Sir David Higgins' proposals for HS2 had the "strong support" of the government.
The government has also scrapped a proposed £700m scheme to link HS2 with the existing HS1 route to Brussels.
The government will instead look at other ways of linking HS2 with the continent.
Chief Executive of business representatives Camden Town Unlimited, Simon Pitkeathley said it was fantastic news and a victory for common sense.
Robert Latham of HS2 Euston Action Group says residents face a 10-year "living hell".
McLouglin confirms he's scrapping the HS2/HS1 link by removing it from the Parliamentary bill. @itvlondon
Transport Secretary Patrick McLouglin says he wants to see historic Euston arch rebuilt. @itvlondon
Anti-HS2 organisation HS2 Action Alliance said while the revamped Euston plan would merely "bring more work and wealth into London while compounding the problem of 100,000 commuters standing every day (while travelling) into London."
HS2 Ltd chairman Sir David Higgins has called for a larger development at Euston - the project's southern terminus.
Euston is the HS2 London terminus and there have been various changes to the original plans, with concerns expressed about the effect of the development on the area which includes the famous Camden market.
Sir David said today:
"I propose the Government should look at a more comprehensive redevelopment of Euston - a solution that could truly stand the test of time and allow the station to join St Pancras and King's Cross as an iconic driver of local regeneration whose beneficial effects will be felt for generations."