TV chef Delia Smith, the singer Olly Alexander and the former deputy prime minister Michael Heseltine are among public figures contributing to the cost of coach travel to a march calling for a referendum on the final Brexit deal.

They have agreed to pay more than £1,000 each for buses taking supporters from across the country to the “people’s vote” demonstration in London on 20 October.

Others sponsors include the actors Sir Patrick Stewart and Natascha McElhone, the millionaire co-founder of Superdry, Julian Dunkerton, the author Ian McEwan, the former foreign secretary David Miliband and his former Labour government colleague Peter Mandelson.

Alexander, the lead singer of the Years & Years, who is paying for travel from the Forest of Dean, is urging young people to turn out in force.

“This is our future we are talking about, and we have to be able to have a say. The will of the people can change, and I believe it has as we have watched the mess unfold,” he said.

Campaigners are hoping that at least 100,000 people will show up for the march, which takes place two days after the scheduled deadline for the Brexit deal to be signed with the EU.

A second referendum can only be held after legislation is passed, and it is opposed by Theresa May, who has repeatedly said her duty is to deliver the result of the vote on 23 June 2016.

Experts have said it would be difficult to hold a another referendum before 29 March, the scheduled day for the UK to leave the EU. But this has not deterred campaigners who point out the process could be shortened or the leave date moved until the public has been given a vote on the final deal.

The Conservative remainer Anna Soubry, MP for Broxtowe, is among those funding a bus to the demonstration, as well as Lord Heseltine, who served under Margaret Thatcher and was later one of the driving forces behind the creation of the single market in 1993.

Rebel Tory MP Philip Lee is paying for a bus from his constituency of Bracknell.

Smith is sponsoring a bus from Norwich, where she is joint majority shareholder in the city’s football team.

The historian Dan Snow is paying for a coach from Southampton, while Stewart is sponsoring one from his home town of Huddersfield.

Smith said, “I am petrified at the way Brexit is going. I’m afraid the political leaders have made a dog’s dinner of it and none of us really trust them any more to take final decision – whatever the result of the negotiations.”

Alastair Campbell, Tony Blair’s former director of communications who is an adviser to the People’s Vote campaign, is funding a bus from Burnley. He said: “In her conference speech Theresa May dismissed the people’s vote as a campaign by politicians. Not for the first time, she is totally misreading the mood of the country. It is not a politicians’ campaign – if only.

“This is a movement of people of all backgrounds and all regions who see Brexit going wrong and want a say on the outcome of the negotiations, whether there is a deal or not. And the fact she felt the need to mention it at all shows how far we have come in so short a time.”

• This article was amended on 8 October 2018 to remove an incorrect reference to Burnley being the home town of Alastair Campbell.