MPs and peers will be sent a roadmap next week detailing how they could stop Brexit by the George Soros-backed Best for Britain group, which has amassed £2.3m in donations to spend on a nationwide lobbying effort to persuade parliament to change its mind.

The group will publish a timetable as part of its “campaign manifesto” at a launch event on 8 June saying that MPs need to introduce amendments calling for a second referendum on the final deal secured by Theresa May in which remaining in the European Union is an option on the ballot paper.

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Best for Britain says it is theoretically possible for a referendum to be held within 17 working days of parliament legislating for one, meaning it could be held in December. But the pressure group says the EU would allow the UK to have a second referendum as late as February or March.

Eloise Todd, the chief executive of Best for Britain, said a second referendum was necessary to ultimately settle the question of whether the UK should leave the EU: “We think people should have a chance to compare the deal we can get to the one we already have. What’s clear is we can’t have ‘a best of all worlds’ illusory Brexit as the debate about the Irish border shows.”

To have any chance of success, Best for Britain would have to win over Labour’s front bench, plus more than 10 Tory rebels and shore up the support of sceptical backbench Labour MPs in constituencies that voted for leave in the 2016 referendum.

The pressure group is stepping up its efforts to lobby 50 MPs by trying to generate pressure on them in their constituencies. It intends to take out advertisements in regional and local papers, starting on Saturday in the Scotsman, and buy up billboards in the target constituencies “as near to MPs’ offices as possible”.

Facebook Twitter Pinterest Eloise Todd, the Best for Britain chief executive Photograph: Suki Dhanda/The Observer

Campaign adverts, which have already appeared in London, Birmingham, Manchester and Liverpool as well as in some national newspapers, are headlined “When will we know what we voted for?” and add: “We all deserve a final say on the Brexit deal”.

Best for Britain said it would spend £500,000 of its £2.3m in donations on the newspaper and outdoor advertising campaign.

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The largest donor has been Soros’s Open Society Foundation, which has provided £800,000. He will not be attending next week’s launch event, but the 87-year-old financier and philanthropist gave a speech in Paris on Tuesday in which he trailed the launch, saying that Brexit was “an immensely damaging process”. He added: “Ultimately, it’s up to the British people to decide what they want to do. It would be better, however, if they came to a decision sooner rather than later.”

Labour MPs in targeted leave-supporting areas include Caroline Flint, the Don Valley MP. She supported remain in 2016 but wrote last month that the UK should respect the referendum result and that parliament should stop “game playing” and reject proposals for a second national vote. Others in the campaign group’s focus include Ian Austin in Dudley North and the newly elected Gareth Snell in Stoke-on-Trent Central.

Conservative MPs being targeted include John Stevenson, who holds the seat of Carlisle with a majority of 2,599 from Labour. Best for Britain says that future investment by multinational tyre maker Pirelli at a plant in the city remains at risk, unless the UK can at least remain part of a customs union with the EU.

The pressure group believes the majority of the British public are turned off by the Brexit debate and will only seriously re-engage once the prime minister has concluded her divorce negotiations with the EU. It is trying to train local organisers to organise street stalls or petitions with a target of having 20,000 conversations with members of the public in the 50 target seats.

The involvement of Soros in the campaign has been attacked by rightwing newspapers, with the Daily Mail describing the Hungarian-American as a “foreign billionaire” engaged in a “plot to subvert Brexit”. Best for Britain uses that coverage as part of its fundraising campaigns, encouraging people to donate and “help us take on the Daily Mail” on a gofundme page that has raised £56,000 in the past week.

Todd said: “The will of the people can be subverted by the will of the people in a second referendum. People can take a new decision based on new information.”

The campaign group is not covered by Electoral Commission regulations, which ban foreign donors, because there is no pending national vote. However, a spokesman said the group did not take money from overseas and that Soros’s donations come via the Open Society Foundation’s UK branch, which is a company registered in England and Wales, which would mean they were permissible under election law.

The campaign group hopes that several dozen MPs will attend the launch event, although does not intend to use any of its existing supporters as principal speakers. Labour MPs such as David Lammy and Jo Stevens have acted as spokespeople before, as well as Green party MP Caroline Lucas and Conservative Dominic Grieve.