Thousands of pro-EU marchers have begun a walk from Pall Mall to parliament to demand a referendum on the terms of Brexit two years on from the vote.

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The People’s Vote protest, running from Pall Mall to Parliament Square, has been organised by increasingly well-funded anti-Brexit groups based at Millbank Tower and led by Open Britain, the successor to the remain campaign.

A People’s Vote spokesperson said the two years since the referendum had been characterised by “arcane parliamentary manoeuvres about this amendment or that amendment” and it was time to take the issue “beyond Westminster and back to the people”.

It comes as pro-Brexit cabinet ministers attempted to pressurise Theresa May to deliver a hard Brexit and not to hesitate from abandoning talks with Brussels.

Writing in the Sun, Boris Johnson said the prime minister must ensure a “full British Brexit”, while Liam Fox said the UK was not “bluffing” about being prepared to walk away from talks with Brussels. David Davis told the Express that there is “lots going on” to make sure the government was ready in case negotiations collapsed.

Their party colleague, Anna Soubry, will be among the speakers at the London march along with the Labour MP David Lammy and the Liberal Democrat leader, Sir Vince Cable, while the campaigner Gina Miller and the actor Sir Tony Robinson will also address those present from 2pm.

Their protest will be opposed by a far-right UK Unity and Freedom march, which will start in Victoria at 2pm and head to College Green, near Parliament Square. It is expected to be smaller, with a few thousand people attending. Promoters say it will “focus on freedom from the EU, freedom from terror, freedom of speech, freedom from sharia law and unity of all people irrespective of race or creed”. Gerard Batten, the Ukip leader, is expected to be present, but not the former leader Nigel Farage.

Police also expect members of the far-right English Defence League and the anti-Islam group Pegida to show up at a march that will conclude a few hundred metres away from where the People’s Vote event will end, and near an Eid celebration in Trafalgar Square.

Anti-Brexit campaigners are focused on trying to create popular support for a referendum on whatever deal Theresa May achieves in negotiations with the EU. Polling and focus group work led Open Britain to use the phrase People’s Vote in calling for a final referendum, in which remaining in the EU would be an option on the ballot paper.

A poll on Friday, conducted by Survation for Good Morning Britain, found 48% of respondents supported a referendum on the final deal, while 25% were opposed. A majority of those asked also said they would support remaining in the EU by 53% to 47% if a referendum were held today.

The People’s Vote campaign is also highlighting the role of ordinary citizens, with Ciaran Donovan, a delivery driver from Romford, east London, expected to appear on stage to sign a petition demanding a referendum on the final deal. The roughly £100,000 cost of the protest was raised over seven days by a crowdfunding campaign.

In his speech, Cable is expected to say that overwhelming ambition must be to stop Brexit. “Parliament is fiddling at the margins while the country slowly burns … Better to stop the damage. To return the issue to the people – to vote on the deal.”

The George Soros-backed group Best for Britain has been separately campaigning for a second referendum, focusing on newspaper and outdoor advertising, and local campaigning in parliamentary seats where they hope to persuade the sitting MP to support an amendment for another vote. It is encouraging supporters to attend the People’s Vote march.

