Campaigners against Theresa May’s “my deal or no deal” Brexit strategy are planning to mobilise the public and politicians for a showdown over the UK’s future in Europe in the final six days before Britain is due to leave the EU, the Observer can reveal.

The plans will involve a huge march in London on Saturday, 23 March, aimed at demonstrating the scale of public anxiety about the two Brexit options May is offering, which will conclude with speeches outside the Palace of Westminster. Hundreds of thousands are expected to attend. Then on 25 and 26 March, MPs of all parties say they will be ready to rally behind a “lethal” amendment that will allow May’s deal to be passed, but only on condition that it is first ratified and approved by the British people in a referendum. Such a referendum would require article 50 to be delayed.

If the British people reject May’s deal in that second public vote, the UK would in all probability stay in the EU on its current terms.

MPs who backed Remain in the 2016 referendum – and who are appalled by May’s attempts to “run down the clock” in the hope of forcing parliament to vote for her hugely unpopular deal – believe that the two-pronged approach of involving the public and politicians has a good chance of averting a disastrous Brexit outcome, albeit at the 11th hour.

While some at Westminster believe the chances of securing a second referendum have faded, supporters of the latest plans say the Commons will be most likely to back another public vote at the moment when a nervous nation will be on the brink of the biggest decision in its postwar history, one that will affect the futures of millions of British people. The UK is due to leave the EU on 29 March.

On Saturday one of the strategists behind the planned amendment, the Labour MP Peter Kyle, said that the shadow chancellor, John McDonnell, and the shadow Brexit secretary, Keir Starmer, were enthusiastic about the plan and looking at whether Labour could whip for his amendment.

“I know they are both warm to the idea,” Kyle said. “In the next few days they will be testing how wide support for this amendment is in the party.”

Another senior Labour MP involved in talks about what is being called parliament’s “final showdown” said: “By that stage, at one minute before midnight, Labour will have no option but to back the Kyle amendment as a route to a second referendum, as they will have run out of alternatives. There should also be enough Tories who will see the sense in allowing the public either to sign off on, or reject, May’s deal. This is clearly the best way to end this argument for good.”

The shadow Scotland minister, Paul Sweeney, threw his support behind the strategy at a meeting of Labour MPs last week on Thursday entitled “Love Socialism, Hate Brexit”. He said: “It’s not about a people’s vote. It is not about overturning any view.”

Florists: Fresh blooms could become preserve of the rich in no-deal Brexit Read more

Sweeney added that, if May was so confident her deal was the best one available, she should be willing to test it against public opinion, in the same way that the Irish peace process was subject to ratification by the people of Northern Ireland and the Republic in 1998. “If Theresa May is not willing to compromise on her deal, then if she’s that confident in it she should approach it the same way as the Good Friday agreement, so there was a ratification … We give the people a final say.”

Most MPs believe the prime minister will try to leave a final crucial Commons vote on her deal until the last possible moment, probably early in the week after she returns from an EU summit in Brussels on 21 and 22 March. But that eventual “meaningful vote” – likely on 25 or 26 March – would be amendable, giving those MPs who believe the issue must be put back to the people their opportunity to strike.

Labour’s Yvette Cooper and Conservative Oliver Letwin plan to table an amendment in the next fortnight that would force May to apply to the EU to extend article 50 for an unspecified period beyond 29 March if the prime minister has not secured parliamentary backing for a deal by the middle of March. But supporters of another referendum say the final piece of the jigsaw will be to get MPs to support another public vote during the extension period.

This week May and Labour leader Jeremy Corbyn – both facing splits within their own parties and possible resignations over Brexit – will hold talks with European leaders in an attempt to find a breakthrough. But hopes that the two leaders can agree on a cross-party way forward are fading, not least because of the prime minister’s refusal to accept Labour’s central demand for a UK-wide customs union and her opposition to taking the option of no deal off the table.

In October an estimated 700,000 people from all over the UK marched peacefully on parliament to demand a second referendum on Brexit. The event was the biggest outpouring of public opposition to government policy since the anti-Iraq-war protest in 2003.

The event on 23 March will be entitled “Put It to the People”, and the organisers say it will be for all those people who want to stop a disastrous Brexit, not just dyed-in-the-wool Remainers who have always been wedded to the idea of reversing the referendum decision.