Cross-party rebel MPs said they had new optimism that measures to stop a no-deal Brexit could pass both the Commons and the Lords before parliament is prorogued, as Labour’s Tom Watson confirmed a potential bill had been drafted.

Sir Oliver Letwin, one of the leading Conservative architects of plans to stop no deal, has said MPs do have time to pass legislation on it.

However, MPs from different parties are believed to be still at odds over how to stop Boris Johnson from circumventing any new law – and crucially what the aim of any extension to article 50 should be, whether that be extra time for negotiations, a second referendum or a general election.

Watson, who announced on Friday he was joining a legal challenge to stop the prorogation of parliament, said concrete plans were now in place.

“I have taken advice on legislative solutions to challenge the prime minister’s action to stop us crashing out of the EU without a deal,” he said. “I am in discussion with colleagues in other parties and a bill to achieve this outcome has been drafted.”

Letwin, who led efforts to stop no-deal Brexit this year by passing a bill with the Labour MP Yvette Cooper, said “there probably is time” to get a measure to block a no-deal Brexit through parliament, involving MPs seizing control of the order paper to pass the bill in a matter of days.

Facebook Twitter Pinterest Tom Watson said he was joining a legal challenge to stop the prorogation of parliament. Photograph: Luke Dray/Getty Images

Opposition peers expect Tories in the Lords to attempt to filibuster the legislation, which must have passed through all its parliamentary stages and received royal assent before parliament is suspended or it will fall.

The Labour leader in the upper house, Angela Smith, has been taking advice on procedural mechanisms for ensuring the government cannot prevent peers from sitting for as long as it takes to get the bill through. Labour peers have been put on a three-line whip for Wednesday to Friday next week.

A Labour source in the Lords said: “If the Commons does pass the bill, the government should be in no doubt that the Lords will do all it can to protect the will of the elected house.”

In the Commons, a number of prominent Conservative MPs, including the former cabinet ministers Philip Hammond, David Gauke and Rory Stewart, have indicated they will back the efforts next week but Letwin said he was not complacent about numbers.

“It’s a foolhardy person who predicts the number of MPs who will vote either way on an issue of this kind and we will just have to see whether we can acquire a majority of the required kind,” he said on Friday.

“I know that there are a number of my colleagues who feel – as I do – that a disorderly no-deal exit is a very bad idea, and they have in the past been willing to come and support efforts to prevent that happening and I very much hope that will happen again.”

A senior MP close to the rebels’ discussions said all efforts would be focused on passing a bill forcing the government to request an extension, but there were still question marks over how long an extension should be and for what purpose.

“Labour and the frontbench want a general election, soft-Brexit Tories like Letwin don’t want either a people’s vote or a general election and a significant number of the PLP [parliamentary Labour party] won’t vote for a referendum either,” the MP said.

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“If the legislation is vague, as it was in the Cooper bill in April – where the extension length was unspecified – Boris could simply ask for another six hours’ extension and satisfy the legal requirement.”

Letwin denied reports that the Commons Speaker, John Bercow, had broken off his family holiday to discuss “cooking up plans” with him to stop parliament being prorogued but said the pair had been in contact.

“There’s no question of any MP cooking up any deal with the Speaker. You cannot do that. The Speaker has to follow the rules,” he told BBC Radio 4’s Today programme.

But he added: “I have talked to the Speaker and the clerks on many occasions and will continue to do so.”

On Friday, Johnson told MPs that efforts to stop no-deal in parliament were detrimental to his attempts to secure concessions from the EU.

“I’m afraid that the more our friends and partners think at the back of their minds that Brexit could be stopped, that the UK could be kept in, by parliament, the less likely they are to give us the deal that we need,” he said.

Play Video 1:37 Boris Johnson suggests prorogation will help negotiate Brexit deal with EU – video

“And so that’s why I really hope that MPs will allow the UK to do a deal and to get ready for a no-deal Brexit – and that’s the best way forward for our country.”

EU officials remain concerned that the UK has so far presented no concrete proposals for replacing the backstop – the insurance policy for avoiding a hard border in Ireland, which Johnson has described as undemocratic.

Johnson hopes to strike a deal at a key meeting of the European council on 17 October, and will then give MPs the chance to vote on it the following week, just days before the Halloween Brexit deadline. He insisted they would have “a lot of time” to debate the issues.

“We’re coming up to the last period before we leave on 31 October, and in that period, parliament is going to have a lot of time, still – and they’ve spent three years debating Brexit by the way, without actually getting it over the line,” Johnson said.

“They’re going to have a lot of time for consideration, and what I want to do now, which I think is what most people in the country want the government to do, is get on and try and get an agreement, but if we can’t get an agreement, get ready to come out anyway.”