The small group of mainly Conservative MPs are being targeted because they have been particularly vocal in their support of cutting all ties with Brussels, including leaving the single market.
Labour’s Kate Hoey and high profile Tories including Iain Duncan Smith are on the “attack list” drawn up by the Remain-supporting group Open Britain.
Activists have also drawn up a list of 20 staunchly pro-European MPs from across the three main political parties, as well as Green MP Caroline Lucas, who they plan to defend in the 8 June vote.
Labour's Mary Creagh and Conservative Neil Carmichael are among the MPs to win the support of Open Britain’s election plan, dubbed the 20/20 key seat strategy.
The group says it will draw on the 500,000 supporters it has on its books and has teamed up with European Movement and Britain for Movement to access another 100,000 backers.
Lord Mandelson, who sits on the Open Britain board, said: “Election candidates of all parties should be demanding that a hard Brexit is rejected and making clear that they will reserve judgment on the outcome until they see whether we get exactly the same trade benefits, as [Brexit secretary] David Davis has promised.”
Ms Hoey, the only Labour MP on the attack list, will face a concerted effort to have her 12,000 majority overturned by the Liberal Democrats.
The party finished more than 20,000 votes behind Ms Hoey in 2015, with just 6.9 per cent of the vote compared with the Labour MP's 53.8 per cent.
But the local borough, Lambeth, backed remaining in the EU by 78 per cent, meaning there is likely to be strong support for a candidate who could oust the Brexit-backing incumbent.
Meanwhile, in his second intervention in the week-old election campaign, Tony Blair said the Conservatives' position on Brexit must be "turned against them".
The Labour former prime minister insisted he had "not urged tactical voting" after suggesting voters may support Lib Dems or Tories if they kept an open mind on EU exit negotiations.
“We have to expose the fact that the mandate the Tories are asking for is not for an open negotiation in the interests of the country but for a "Brexit at any cost" driven by the ideology of the right of the Tory party,” he wrote, in an article for The Guardian.