The row about high energy prices has been ignited after British Gas announced its profits had doubled in the first half of this year.
It comes as its parent group Centrica said it would be axing 4,000 jobs, not all of which will be in the UK.
The cut follows a strategic review aimed at delivering savings of £750 million a year by 2020.
British Gas profits were £528 million for the first half of the year, more than it made in the whole of 2014, even though it recently cut prices by 5%.
Which? executive director Richard Lloyd said: "While it's good to see the new commitment from Centrica to focus on serving customers, with British Gas profits high and wholesale prices low, customers will no doubt wonder why cuts to their bills haven't gone further, and haven't included electricity.
"Following the Competition and Markets Authority's blistering assessment of this sector, we expect big suppliers to pass on falling costs to their customers quickly and fairly."
Profits at engine maker Rolls-Royce slumped by almost a third in the first half of 2015, dropping more than £200 million since the same time last year.
Underlying profit before tax was £439m, down from from £646m at this point in 2014 - a drop of 32 per cent - while revenue fell from £6.5bn to £6.3bn, a three per cent fall.
Earlier this month, Rolls-Royce issued its third profit warning in a year, citing weak demand for its aircraft engines.
But despite the latest fall, chief executive Warren East said the company was still on track to hit its 2015 full-year guidance.
Centrica is to axe thousands of jobs following a strategic review, it was announced today.
The British Gas owner said it was reducing its headcount by 6,000 across the group, not all in the UK.
But the company will create 2,000 other jobs so the net effect will be 4,000 job losses.
British Gas' operating profit was up by 44%, according to today's interim first half results from the group, which was larger than expected.
The company said this was because of a colder year compared to 2014, with consumption up by 11%.
Around 6,500 jobs will be axed at Royal Dutch Shell this year as the oil giant struggles amid a slump in prices, it was announced today.
The firm said it was "planning for a prolonged downturn" by cutting costs by 10 per cent - some $4 billion (£2.6bn) - during 2015, with further cost-cutting expected for 2016.
Investment for the year is also being slashed by a fifth, or $7bn (£4.5bn), with chief executive Ben van Beurden adding: "We have to be resilient in a world where oil prices remain low for some time, whilst keeping an eye on recovery."
Gas giant Centrica is set to announce heavy job losses when it unveils its latest financial results today.
There is speculation that the British Gas owner will cut up to 2,000 posts, with management positions likely to be included.
Asset sales and cost reductions are also likely to be announced by the company, which employs 37,500 workers globally and has 27.9 million customer accounts.
The results will be announced by chief executive Iain Conn, who took up the post in January.
Barclays has announced a 25% rise in first half year profits just three weeks after chief executive Antony Jenkins was fired over lacklustre revenue growth.
It comes despite the bank having to pay out more than £1 billion in compensation to customers over scandals such as PPI mis-selling.
However, the bank has said it will streamline the business to ramp up growth and squeeze costs but has yet to say how they will do that.
The Prime Minister has urged south-east Asian investors to pump money into the cities of the "Northern Powerhouse".
As part of his four day trade mission to the region, David Cameron told investors in Singapore that he wanted them to look at the UK "in a new way" and consider cities like Leeds and Manchester for their plans rather than just London.
I really would encourage you to look at Britain in a new way...
We want to re-balance our country and we want Singaporean and other south-east Asian investors to help us do it. That is what the Northern Powerhouse is all about.
From the North Sea to the Singapore Strait, let's get more trade flowing.
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