Whitehall sources confirmed the prime minister and Chancellor Nadhim Zahawi have given the financing go-ahead for the construction of the Sizewell C nuclear reactor in Suffolk.
Private funding will be sought for the project estimated to cost £20-30 billion.
The Government is then set to make a final decision on public investment early next year, with it expected to buy a 20% stake in the plant, costing up to £6 billion.
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Business Secretary Kwasi Kwarteng, who is tipped to be Ms Truss’s chancellor if she wins the Tory leadership race, is said to be “massively” on board with the plan.
But her camp did not appear to be united on the issue, with Chief Secretary to the Treasury Simon Clarke raising concerns with Mr Johnson and Mr Zahawi.
In a letter leaked to the Sunday Times, Mr Clarke suggested that acting now would tie the hands of their successors.
Mr Clarke, who is expected to get a senior Cabinet job if Ms Truss wins, said the costs of Sizewell C is “sufficient to materially affect spending and fiscal choices for an incoming government, especially in the context of wider pressures on the public finances”.
While essentially a caretaker prime minister, after being forced to resign over a succession of scandals, Mr Johnson previously said he would not be making major decisions before leaving office.
Ms Truss, the frontrunner to replace Mr Johnson on September 6, has pledged tax cuts, including a reversal of the national insurance hike costing at least £30 billion per year.
But she is under growing pressure to offer further support to the most vulnerable, as experts warn the energy price cap could surpass £6,000 next April in a further painful hike.
Mr Kwarteng, in an article for the Mail On Sunday, promised “help is coming”, but insisted it is “entirely reasonable not to detail the exact shape of that support” until later.
He also stressed the need to “crack on with more nuclear power stations” in order to increase Britain’s energy security.
The Stop Sizewell C campaign group said: “Whatever way you look at it, this is a very dodgy decision.
"Has it been made by a lame duck PM who is not supposed to tie the hands of his successor, or was it in fact made before Sizewell C was granted planning consent, lending serious weight to our conviction that this was a prejudiced, political decision?
“Our next prime minister should call Sizewell C in. There are so many better ways to spend billions of pounds of taxpayers’ money than on a project that won’t light a single lightbulb for at least a decade.”
Development consent for Sizewell C was given the go-ahead by Mr Kwarteng in July, but negotiations over the financial investment decision were ongoing.
A Government spokeswoman said: “Nuclear power has a key role to play as we work to reduce our reliance on fossil fuels and exposure to volatile global gas prices.
“Negotiations are still ongoing on Sizewell C and as these are active and commercially sensitive discussions we cannot comment further.”