A legal action has been launched in Scotland aimed at forcing Boris Johnson to ask the EU for an extension if the UK is heading for a no-deal Brexit.
A bill was passed at Westminster which would require the prime minister to write to European leaders if deal is not agreed by 19 October.
But the prime minister said he would "rather be dead in a ditch" than ask for a further delay beyond 31 October.
The latest legal action is being taken in Scotland's highest court.
The petitioners want the Court of Session to use its powers to effectively sign the letter to the EU on the PM's behalf if he refuses to do so.
The action has been taken by businessman Dale Vince, QC Jo Maugham and SNP MP Joanna Cherry.
Earlier this week judges at the same court ruled that Mr Johnson's suspension of the Westminster parliament was unlawful.
The government has lodged an appeal against this ruling, which will be heard by the Supreme Court next week, and Mr Johnson has denied lying to the Queen.
MPs passed legislation shortly before parliament was suspended which aims to stop the UK from leaving the European Union without a deal on 31 October.
The cross-party bill requires the prime minister to write to European leaders requesting an extension to that deadline unless parliament agreed to a deal by 19 October.
Mr Johnson - who has repeatedly pledged to take the UK out of the EU no later than the end of October - said he would "rather be dead in a ditch" than ask for a "pointless delay" to Brexit.
Foreign Secretary Dominic Raab has said the government would "want to test to the limit" what the "lousy" legislation "lawfully requires".
The latest proceedings have been brought against Mr Johnson personally at the Court of Session.
Those behind the case want the court to use a special power - the "nobile officium" - to effectively sign the letter to the EU on behalf of the prime minister, should he refuse to do so himself.
Mr Vince said this would "prevent a no-deal exit on October 31 and make the prime minister abide by the letter of the law, which he's suggested time and time against he's prepared to ignore".
He added: "I've personally been on the receiving end of injunctions that stopped legitimate protests from taking place, so it must be possible to prevent serious law breaking by the PM in the same way."
Mr Maugham said he hoped the court would "deal with the matter speedily".
Other MPs have also said they are preparing legal action in case Mr Johnson refuses to seek a delay to Brexit.
Mr Johnson has insisted that an agreement can still be struck with European leaders at a summit in October, avoiding the need for either an extension or a no-deal exit.
He said: "I'm very hopeful that we will get a deal at that crucial summit. We're working very hard - I've been around the European capitals talking to our friends.
"I think we can see the rough area of a landing space, of how you can do it - it will be tough, it will be hard, but I think we can get there".
The EU's chief negotiator, Michel Barnier, said his side was still waiting to see proposals from the UK to resolve the issue of the border in Northern Ireland.
He told reporters in Brussels: "We are still ready to examine objectively any concrete and legally operational proposals from the UK."