Downing Street would be wrong to think it is too late for MPs to stop a no-deal Brexit, Labour has said.

The shadow health secretary, Jonathan Ashworth, said on Sunday he did not accept a claim, attributed to Dominic Cummings, Boris Johnson’s key adviser, that even if MPs were to pass a vote of no confidence in the prime minister in the autumn, the electoral timetable means any general election would not take place in time to stop the UK from leaving the EU on 31 October.

“There will be opportunities for us when parliament returns in September to stop no deal,” Ashworth told Sky News.

The issue of what is or is not possible in September is crucial because Johnson has said he is determined to take the UK out of the EU at the end of October come what may. A majority of MPs oppose a no-deal Brexit, but opinion is divided as to whether they can mobilise in September to stop this happening.

According to the Sunday Telegraph (£), Cummings has told colleagues it is too late for MPs to use a no-confidence vote to deliver a change of government before 31 October. “If there is a no confidence vote in September or October, we’ll call an election for after 31 October and leave anyway,” Cummings has reportedly said.

Quick Guide What Vote Leave leaders really said about no-deal Brexit Show Boris Johnson, prime minister Johnson told the Treasury select committee in March 2016: “Our relationship with the EU is already very well developed. It doesn’t seem to me to be very hard … to do a free trade deal very rapidly indeed.” Speaking at a Vote Leave event in March 2016, Johnson said: “I put it to you, all those who say that there would be barriers to trade with Europe if we were to do a Brexit, do you seriously believe that they would put up tariffs against UK produce of any kind, when they know how much they want to sell us their cake, their champagne, their cheese from France? It is totally and utterly absurd.” Johnson, then foreign secretary, told the House of Commons in July 2017:“There is no plan for no deal because we are going to get a great deal.” Dominic Raab, foreign secretary Two months before the June 2016 referendum vote, Raab told Andrew Neil on BBC Sunday Politics: “We’re very well placed, and mutual self-interest suggests we’d cut a very good deal and it’s certainly not in the European’s interests to erect trade barriers.” During an appearance on the BBC’s Daily Politics in April 2016, Raab added: “The idea that Britain would be apocalyptically off the cliff edge if we left the EU is silly.” Michael Gove, chancellor of the duchy of Lancaster In April 2016, Michael Gove said the UK would have the best of both worlds. “Outside the EU, we would still benefit from the free trade zone which stretches from Iceland to the Russian border,” he said. “But we wouldn’t have all the EU regulations which cost our economy £600m every week.” Liam Fox, former international trade secretary After the referendum, in July 2017, the then-international trade secretary Liam Fox said: “The free trade agreement that we will have to do with the European Union should be one of the easiest in human history. We are already beginning with zero tariffs, and we are already beginning at the point of maximal regulatory equivalence, as it is called. In other words, our rules and our laws are exactly the same.” Simon Murphy and Frances Perraudin

This view is based on an analysis from the House of Commons library saying that, because of the timetable for an election following a vote of no confidence under the Fixed-terms Parliament Act (FTPA), the vote would have to be on Tuesday 3 September for an election definitely to take place before 31 October.

For a debate to take place on 3 September, the first day back after the summer recess, Jeremy Corbyn, the Labour leader, would have had to table a no-confidence motion before recess. But that did not happen.

In his interview on Sky, Ashworth did not address the argument about the timing of a no-confidence motion, but said other mechanisms would be available to MPs in the autumn.

“Let’s see what happens in September,” he said. “Because the government will have to bring forward appropriate legislation to prepare for this Brexit no-deal exit that they want. And we will use all the means available to us, working across the parties – because we know there are plenty of Tory MPs who want to block no deal as well, particularly a lot of those who Boris Johnson, perhaps rather foolishly in retrospect, sacked from the cabinet two weeks ago.

“We’re working with MPs across the House of Commons, and we will work to stop no deal.”

Dominic Grieve, the Conservative former attorney general, told the BBC that Cummings would be right to say there were “a whole series of obstacles” facing MPs like himself trying to stop a no-deal Brexit. But he claimed Cummings could be “missing the point that there are a number of things the House of Commons can do, including bringing down the government and setting up a new one in its place.”

Although some MPs are looking intently at what parliamentary devices could be used to stop no deal, and John Bercow, the Speaker, has indicated that he he will allow votes on this issue, the Institute for Government published a briefing earlier this year saying these mechanisms would have little chance of success. That is because stopping no deal might have to involve asking for a further delay to Brexit, or revoking article 50, and both those decisions are in the hands of the prime minister.

A no-confidence vote has been seen as the best means of stopping no deal. Even if it were to lead to a general election taking place on or after 31 October, opposition MPs would argue that in those circumstances Johnson would be under an obligation to seek an extension of article 50 because the cabinet manual says, during an election, the government should be operating in caretaker mode, and not taking decisions that would bind its successor.

But Cummings has reportedly told colleagues Johnson would refuse to request an extension in those circumstances.

The one scenario that would stop no deal would be if a no-confidence vote were to lead not to a general election but to the formation of a new government that could win a vote of confidence within the 14-day period allowed under the FTPA. This would require a coalition of MPs to unite behind either Corbyn or someone willing to lead a government of national unity.

But the FTPA does not say anything about what the process might be for establishing whether such a coalition exists, and as yet there is no evidence the opposition parties are willing to unite in this way in the autumn.

Downing Street declined to comment when asked about Cummings’s views on MPs being able to stop a no-deal Brexit.

In a separate development, Stephen Barclay, the Brexit secretary, has used an article in the Mail on Sunday to urge Michel Barnier to seek a new negotiating mandate from the EU 27 because the UK will not accept a Brexit deal involving the backstop.

In the article, which is published under the headline “You don’t have a mandate now, Monsieur Barnier. Go back to your EU masters”, Barclay argues that the “political realities” have changed since the EU set out its negotiating mandate for Barnier to follow.

“Since the last mandate was agreed, 61% of all the EU states’ MEPs have changed. Such a fundamental shift illustrates the need for a change of approach,” Barclay writes.

“Mr Barnier needs to urge EU leaders to consider this if they too want an agreement, to enable him to negotiate in a way that finds common ground with the UK. Otherwise, no deal is coming down the tracks.”

Johnson has said repeatedly that the backstop – the mechanism intended to keep Northern Ireland aligned to EU single market and customs rules, to prevent the need for border controls with Ireland if the final Brexit outcome does not achieve this – must be abandoned.

The backstop is based on a paragraph in the joint report on Brexit between the UK and the EU that was published in December 2017 when Johnson was foreign secretary.