The campaign group, Best for Britain, wants MPs to introduce amendments calling for a second referendum on the final deal secured by Theresa May.
They also want included on the second referendum ballot paper an option for remaining in the EU.
Eloise Todd, the chief executive of Best for Britain, said another referendum was required to allow people to decide on the final deal offered.
“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,” she said.
“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.”
Best for Britain claim that it would be possible for parliament to hold a referendum within 3 weeks of parliament legislating for one, which means theoretically it could be held as soon as December.
The group is targeting 50 MPs by attempting to generate pressure on them from within their constituencies.
It has earmarked £500,000 of its £2.3m fund to be spent on newspaper and outdoor advertising campaigns.
The group has already began an advertising campaign in London, Birmingham, Manchester and Liverpool with headlines reading: “When will we know what we voted for?” and “We all deserve a final say on the Brexit deal”.
George Soros is an 87-year-old Hungarian-American financier and is the group’s largest backer. The Soros’s Open Society Foundation provided a donation of £800,000 to Best fro Britain.
Mr Soros said Brexit was “an immensely damaging process” in a speech he made in Paris on Tuesday.
The campaign group is not covered by Electoral Commission regulations, which ban foreign donors, because there is no pending national vote.
Although, a spokesman for Best for Britain said the group did not take money from overseas as Soros’s donations came from the Open Society Foundation’s UK branch.
Best for Britain is expected reveal a “campaign manifesto” at its launch event on 8 June and is hoping that several dozen MPs will attend.
Labour MPs David Lammy and Jo Stevens have acted as spokespeople before for the group, along with Green party MP Caroline Lucas and Conservative MP Dominic Grieve.