Nigel Farage, the former Ukip leader who is in temporary charge again, has pledged to lead a 100,000-strong demonstration in London.
He wants to march on the day the Supreme Court considers the next legal phase of the Brexit negotiations.
Farage’s threat poses serious questions for how the left should respond to the setback the Tories suffered last week.
This threw Tory prime minister Theresa May’s timetable into chaos.
The court decided that both the House of Commons and the Lords will have to agree before the government triggers Article 50.
Triggering Article 50 will begin the two years of negotiations to leave the European Union (EU).
The ruling could at the very least slow the process beyond May’s target of moving Article 50 before the end of March 2017.
As well as a flurry of amendments from MPs, the government could face foot-dragging by unelected Lords.
The government is therefore appealing to the Supreme Court, and Farage’s march is designed to pressure the judges to allow the appeal. Amid the confusion Tory MP Stephen Phillips resigned from the Tories and will leave parliament.
Phillips was pro-Brexit but said he was unhappy that the Tories had tried to avoid parliamentary approval for the process.
While an MP, he has topped up his salary by £750,000 a year working as a barrister and judge.
Labour has also been thrown into confusion by the court’s decision.
Labour leader Jeremy Corbyn said on Sunday that Labour MPs would not vote to trigger Article 50 unless the Tories agreed to the party’s “Brexit bottom lines”.
These were British firms’ access to the single market, no watering down of EU workplace rights, and guarantees on safeguarding consumers and the environment.
They also included a promise that, if capital investment is lost as a result of Brexit, then the British government will make up the shortfall.
There is apparently no “bottom line” over freedom of movement of workers.
Corbyn was then contradicted by deputy leader Tom Watson who said Labour would not block Article 50.
Labour’s shadow Brexit secretary Keir Starmer has also said there were no circumstances in which Labour would block Article 50.
The issue of the single market may not sound centrally significant.
But single market rules are precisely those that have been used to smash the anti-austerity struggle in Greece.
They include the regulations used to force through privatisation and prevent nationalisation.
Fight for a left Brexit
Any socialist approach to Brexit has to say clearly that we are for freedom of movement of workers and against membership of the single market. But it’s wrong to try to halt Article 50 in parliament.
There should be debate, campaigning and struggle to shape the type of Brexit that is agreed.
But this must not become an attempt to reverse the referendum result by the back door—as many MPs and liberal commentators would like.
If Labour seeks to find a pretext to vote against Article 50 this will simply strengthen the forces of the racist right.
It will mean the racists find it easier to pose falsely as “champions of the people”.
The answer to Nigel Farage is not to demonstrate against Brexit. Labour and the trade unions have to campaign for a positive vision of a Brexit.
This must include more rights for migrants and refugees, defending and extending workers’ rights, and breaking from austerity policies.