Theresa May was handed a humiliating defeat in parliament by Labour and Conservative MPs who organised to demonstrate the strength of parliamentary opposition to leaving the EU with no deal.

MPs voted by 303 to 296 in favour of an amendment to the finance bill tabled by Labour’s Yvette Cooper to curb some of the government’s tax administration powers in the event of no deal without explicit authorisation for parliament.

The coalition of high-profile MPs behind the amendment are expected to use the victory as a springboard for further parliamentary action to prevent the UK crashing out of the EU.

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Sir Oliver Letwin, the former Tory minister who rebelled to back Cooper’s amendment, said: “The majority tonight that is expressed in this house will sustain itself. We will not allow a no-deal exit to occur at the end of March.”

Twenty Conservatives rebelled against the government, including the former defence secretary Michael Fallon and former education secretary Justine Greening.

Tory MPs were whipped to vote against the amendment, despite rumours that the government would concede. Eleven Tories had signed the amendment, including former cabinet minister Nicky Morgan, select committee chair Sarah Wollaston, former minister Nick Boles and Sir Nicholas Soames.

During his speech in the Commons, Letwin sounded almost tearful as he said he would rebel against the Tory whip. “I will be voting with [Cooper] against my own government, very much against my own will, and I will continue to do so right up until the end of March in the hope we can put paid to this disastrous proposal.”

Privately those behind the amendment’s success concede it may have little material effect on no-deal preparations. Instead, its purpose has been to galvanise MPs across the house and prove there is a parliamentary majority to oppose no deal, which they expect could grow when subsequent amendments are tabled to other bills, which could have wider-reaching consequences.

Speaking in the Commons, Cooper said MPs across the house agreed on the dangers of no deal. “I’m worried we could come to the crunch and parliament will not have the powers to stop [no deal] happening,” she said. “I think we have a responsibility not to just stand by.”

The Labour leader, Jeremy Corbyn, who turned round and applauded Cooper in the chamber as the defeat was announced, said: “This vote is an important step to prevent a no-deal Brexit. It shows that there is no majority in parliament, the cabinet or the country for crashing out of the EU without an agreement. That is why we are taking every opportunity possible in parliament to prevent no deal.”

Labour threw its weight behind the amendment on Monday afternoon, as Treasury officials and Tory whips scrambled to assess the impact it could have on Treasury operations.

Opening the debate, the shadow Treasury minister Jonathan Reynolds said it had the support of the opposition because it was “a chance for parliament to make a clear statement rejecting a no-deal outcome and that is a statement that cannot come soon enough”.

He said that the government had “run down the clock” towards the 29 March exit date. “Nobody should be underestimating at this stage how likely a no deal exit could be,” he said. “The government has got us to the point of ruin.”

Morgan said those who had signed the amendment had different views both on Brexit itself and on the way forward. “It is right that parliamentarians on both sides of the house should rule out the most damaging thing that could happen on 29 March,” she said.

“It would be a gross dereliction of responsibility of members of this house to inflict a no-deal situation on our constituents,” she said. “It is time for members on all sides to make it clear to the government that a no-deal outcome for Brexit is absolutely unacceptable.”

The veteran Tory MP Ken Clarke, a prominent Europhile, said crashing out with no deal would leave the UK “as the only developed country in the world that has no trade agreements at all with anyone and made to fall back on WTO rules, made to sound marvellous by Brexiteers but do not amount to very much.”

Opposition to the rebels’ amendment came from pro-Brexit Labour MP Kate Hoey, who said it would be “irresponsible for the government not to be making contingency plans for a WTO situation…”

Backers of the amendment concede that it cannot, in and of itself, stop a no-deal Brexit from occurring. It is attached to a clause designed to give the government the power to keep some areas of tax administration working in the event of a no-deal Brexit.

Cooper’s amendment meant that new power would only be allowed to come into force if there were either a Brexit deal, a decision to extend article 50, or a vote in the Commons specifically approving a no-deal Brexit.

It is this format of three options that MPs may later decide to attempt to apply to other bills going through the Commons.

A number of bills could be amended, which might have more significant impact on day-to-day government operations. Seven bills must be implemented in order to provide a smooth exit by March, including trade, agriculture, healthcare, financial services, fisheries and immigration, as well as legislation for the withdrawal agreement.

Government sources had briefed that the material effect of the finance bill amendment would be “low down the list” of difficulties if the UK was heading towards a no-deal Brexit and officials suggested that more emergency legislation would probably be needed, where the government could attempt to restore these powers without caveat.

Earlier, May’s spokesman said the amendment was “not desirable but the effect of the amendment on no-deal preparations would be inconvenience rather than anything more significant”.

He said it would not prevent the government from collecting tax. “What clause 89 does is allow the government to make minor amendments to tax law, in consequence of EU exit, in order to keep the tax code working as it currently does,” the spokesman said.

