George Osborne’s authority has been directly challenged by 65 pro-Brexit Tory MPs, who have signed a letter saying they will not back the “emergency” tax-raising budget he said would be necessary if the country voted to leave the EU.

The backbench MPs called the chancellor’s measure a “punishment budget”. The scale of the revolt demonstrates the struggle Osborne and David Cameron will face in picking up the reins of government next Friday after the referendum on 23 June.

The 65 MPs who signed the letter, saying they would refuse to back the measures, include six former cabinet ministers – Iain Duncan Smith, Liam Fox, Owen Paterson, David Jones, John Redwood and Cheryl Gillan. Osborne claimed that a vote to leave would leave a £30bn blackhole, which, he said, would have to be plugged with income tax rises and public spending cuts.

The joint statement said it was incredible that the chancellor could set out proposals reneging on manifesto pledges not to raise taxes.

“If the chancellor is serious, then we cannot possibly allow this to go ahead,” the MPs said. “It would be unnecessary, wrong and a rejection of the platform on which we all stood. If he were to proceed with these proposals, the chancellor’s position would become untenable.”

Crispin Blunt, chair of the backbench foreign affairs committee, said: “There’s no support for this nonsense – and it is nonsense.” Asked whether the chancellor should continue in his job after next week’s vote, he said: “That has to be up to the prime minister.”

Another senior Brexit MP, Bernard Jenkin, said: “[Cameron and Osborne] should take some deep breaths, calm down and remember they are running the country, not just a referendum campaign. They should not be talking up a crisis when there isn’t one. Their campaign has been hugely irresponsible.”

Osborne’s position on immigration was also undermined by Theresa May, the home secretary, who backs remain but is still a possible leadership contender. May, who has kept a low profile in the campaign, told the BBC that the UK should “look at further reform in future” of free movement in the EU – which some senior Labour figures have recently demanded.

Osborne pointed out on Wednesday morning that there was no appetite for this in the EU and argued migration could be controlled through restrictions on welfare.

There was also criticism of Cameron, although the leaders of the Vote Leave campaign have insisted in public that they believe he could remain in post even in the event of a vote to quit the EU and take charge of the negotiations for an exit.

But one senior Vote Leave source told the Guardian the intensity of the campaign had been such that “we think Cameron would be out by lunchtime”.

The chancellor, who remains a contender to succeed Cameron, defended his position on Wednesday and produced a mocked-up budget document to bolster his argument.

“You would have to show the British public you had a credible plan to deal with the public finances,” Osborne insisted. Pressed on whether it would spell the end of his own career, he said: “It’s not about one politician, it’s not about one political career … this is about the future of our country, about who we are as a country. What’s the point of getting involved in public life if you’re not prepared to fight for the things you think are really important to our country and its future, its standing in the world and for jobs and prosperity?”

He is expected to double down on the economic arguments on Thursday, delivering a Mansion House speech in the City of London in which he is expected to underline afresh the financial risks of leaving. A senior remain campaign source said: “He makes no apology for making the economic argument – it is the argument.”

But backbench Conservatives reacted with fury to the mocked-up document, which entailed abandoning a series of key Conservative election pledges, on everything from income tax to inheritance tax.

The Tory MP for Peterborough, Stewart Jackson, said: “Osborne, by his appalling conduct, has lost the confidence of the parliamentary conservative party and the City. His efforts to talk down the UK economy are unprecedented and his petulant threats of a fantasy budget are desperate and risible.” He added: “His position is now untenable.”

Another senior Tory MP in the Brexit camp, who signed the statement against the emergency budget, said the country might need Cameron to stay on for a while to ensure stability if there were a vote to leave but that Osborne was more dispensable. “I think George’s chances of becoming PM have been on the rocks for quite some time, since around the time of tax credits certainly. But this would be hard to come back from. It’s not impossible, after a few years, if there is a vote to remain, but a lot of party members voting to leave are very angry about the way they have been portrayed as little Englanders and unpatriotic by both David and George.”

However, Michael Gove, the justice secretary and a leading Brexit campaigner, dismissed the idea that he would join fellow Tories in voting down an emergency budget called by Osborne, but only because he did not think such a fiscal event would be necessary.

Questioning the judgment of Osborne, who has for years been one of his closest political friends, Gove said in a BBC Question Time interview: “There is no need for an emergency budget. The truth is, if we vote to leave we will be in an economically stronger position.”

The argument arose on a day of drama in Westminster as the Ukip leader, Nigel Farage, and pop star Bob Geldof clashed in the middle of the Thames in boats campaigning for and against remaining in the EU. Farage dismissed the chancellor’s warning. “Ignore Mr Osborne’s fantasy budget. Post-Brexit he won’t be the chancellor for very long,” he tweeted.

Even if the UK votes to remain in the EU, Osborne’s leadership hopes have already been wounded by U-turns over tax credits and disability benefit cuts, and the animosity of much of the Conservative grassroots towards Downing Street’s campaign to stay in.

Osborne stood his ground on Wednesday, however, insisting there would be no choice but to make extremely tough spending decisions to protect the economy.Cameron backed him and the former Labour chancellor Alistair Darling, at prime minister’s questions, saying the financial shock of leaving the EU must not be ignored. “Nobody wants to have an emergency budget. Nobody wants to have cuts in public services. Nobody wants to have tax increases,” he said. “But I would say this. There is only one thing worse than not addressing a crisis in your public finances through a budget, and that is ignoring it.”

The spotlight will switch back to Labour on Thursday, with Gordon Brown and the shadow chancellor, John McDonnell, appearing together in Manchester to make the argument that northern Britain could be entitled to more EU funding if it votes to remain next week. Separately, Labour local council leaders will argue that poorer areas would be hardest hit by the economic shock in the event of Brexit.

Brown will warn that leaving the EU could put Britain’s great cities at risk of industrial decline last seen in the 1980s under Margaret Thatcher. The Labour former prime minister will say the UK’s 10 biggest cities outside London would see their economies threatened by leaving the EU, which has poured funding into areas that the Tories turned “from industrial heartlands into industrial wastelands”.