With a No vote successfully secured senior Conservatives have come out of the shadows to demand that David Cameron renege on his “reckless” promise to maintain Scotland’s generous funding settlement from Westminster.

Under the Barnett formula Scotland gets £10,152 per head of population for devolved public services compared to the £8,529 that is spent in England. In the run-up to referendum Mr Cameron signed a “vow” along with the other party leaders to continue the “Barnett allocation of resources” across the UK.

Privately Tory MPs were furious at the concession but were persuaded not to speak out for fearing of boosting the Yes campaign. However, yesterday their frustration at Mr Cameron’s move was on clear display. Asked about the Barnett formula in an interview the London Mayor Boris Johnson said he was “keen on a Barnett formula that does justice to Barnet with one T”.

He added: “We can’t just go on with a system that even Joel Barnett himself thinks is outdated.”

He suggested Lord Barnett – who devised the system in the 1970s as Chief Secretary to the Treasury and is now 90 years old – be asked to redesign the equation so that the “slightly reckless promise” to keep it could be honoured by maintaining its name.

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The former Environment Secretary Own Paterson was also scathing about the “chaotic manner” in which the No vote had been won which he said had “undermined the strong and resilient UK on which we all depend”.

“It is unacceptable that in the late stages of the campaign an ex-Labour leader was allowed to make rash promises of ‘extensive new powers’ to the Scottish people with the endorsement of all three UK party leaders, but with no mandate from Parliament,” he said.

Mr Paterson added: “Maintaining the Barnett formula, under which the Scottish receive £1,600 per head more than the English, and expecting English taxpayers, who are struggling to make ends meet, to keep footing the bill is unjust.

“Such a lopsided constitutional settlement cannot last; it is already causing real anger across England. If not resolved fairly for all the constituent parts of the UK for the long term, it will fall apart.”

Chris McAleese at Bannockburn Polling Station, as voters go to the polls in the Scottish Referendum (PA)

“The normal autumn routine of party political conferences is not sacrosanct. The Prime Minister’s promise of English votes for English laws is welcome and Parliament should be recalled next week to discuss this and a wider constitutional settlement.”

Bernard Jenkin, the Conservative chair of the Public Administration Select Committee, said he was concerned that Mr Cameron’s vow had been too vague and could be open to misinterpretation.

“We’ve really no idea what these promises of extra powers actually are or what is meant by honouring the Barnett formula,” he said.

Sent out to defend the Government’s position, the Defence Secretary Michael Fallon claimed that the Barnett formula would be less important as Scotland raised more of its revenue through direct taxation.