Labour’s deputy leader, Tom Watson, will address the People’s Vote march on Saturday, saying he is prepared to vote for Theresa May’s Brexit deal in parliament as long she agrees to put it to a second referendum.

The politician will be the most senior Labour figure to address the rally in Parliament Square in the afternoon, following a mass march through central London at which hundreds of thousands of people – and possibly more – are expected to attend.

Breaking away from the carefully crafted Brexit compromises promoted by the party leader, Jeremy Corbyn, Watson will say he has “an explicit message for Theresa May: I will vote for your deal or a revised deal you can agree with my party.

“I will help you get it over the line to prevent a disastrous no-deal exit. But I can only vote for your deal – or any deal – if you let the people have a vote on it too. That’s why I’m proud to be marching. I trust the people I represent.”

The last People’s Vote march in October attracted an estimated 700,000 protesters, and while its organisers are reluctant to say any more than that “hundreds of thousands” are due to attend on Saturday, the expectation is that significantly more will turn up.

Other politicians due to speak at the rally – which is due to run between 2.45pm and 4pm in Parliament Square – include Nicola Sturgeon, Scotland’s first minister, and Michael Heseltine, a former Conservative cabinet minister.

Watson will be the most senior Labour figure speaking at the conclusion of the march, although there will also be speeches from the London mayor, Sadiq Khan, and backbenchers Jess Phillips and David Lammy.

Corbyn is not due to be present at the event, which starts on Park Lane in central London at noon. The Labour leader will be in Morecambe, Lancashire, campaigning for the local elections due in May.

John McDonnell, the shadow chancellor, also said he would not be marching. “Alastair Campbell asked me whether I’d be going along and I said to him very honestly that by going there I might alienate some of the people who are strong leavers who I want to bring on board.”

Facebook Twitter Pinterest Anti-Brexit campaigners take part in the People’s Vote march in October 2018. Photograph: Yui Mok/PA

Watson’s remarks make him the first shadow cabinet figure to publicly back a compromise proposed by Labour backbenchers Peter Kyle and Phil Wilson, in which supporters would allow May’s deal to pass if it was subject to another popular vote.

Kyle hopes to put his amendment down on Tuesday, when May is expected to return her Brexit deal to parliament. Although the Labour front bench have repeatedly discussed the compromise proposal it is not certain the party will support it.

The former foreign secretary David Miliband is due to travel from New York to attend, while a string of leftwing junior shadow ministers and MPs will address a Left Bloc rally at 11am at Stanhope Gate, near the south end of Park Lane. Their numbers include Clive Lewis and Marsha de Cordova.

Public concern about the state of the Brexit negotiations has soared in the days leading up to the march. The electronic petition calling for the government to “Revoke Article 50 and remain in the EU” had been signed by 3.5m people by early evening on Friday, having hit 2m around 10.30pm on Thursday evening. The parliamentary website where the petition is hosted said it would update running totals every half an hour to prevent the site from being overloaded with traffic; insiders added that they were confident that its anti-fraud systems meant that it could ensure the petition was only signed by British citizens or UK residents.

Dozens of Guardian readers said they were planning to go on the march. Robert Busch, a German scientist at the University of Roehampton who lives in London, said: “I came to an open, confident, welcoming, democratic UK with a special status in the EU.

“Brexit has paralysed democratic governance, damaged economy, will worsen inequality, pander to xenophobes. I want to see my adopted home restored.”

Another, Fleur Young, said she was preparing to leave her home in Cornwall to go. “I couldn’t look my grandchildren in the face if I hadn’t done some small thing in my power to try to preserve their rights, freedoms and general future wellbeing.”

Organisers say that those attending should go to the north end of Park Lane, exiting from Marble Arch station because Hyde Park Corner station became too full last time. Giant television screens will also be placed in Trafalgar Square to relay the speeches, in case people don’t complete the 90-minute route in time.

The last People’s Vote march was the second biggest protest this century – the largest was the 2003 Stop the War demonstration against the looming conflict in Iraq. Organisers said up to 2 million people took part, while police estimates put the figure at “in excess of” 750,000.