But Lib Dem health spokesperson Munira Wilson told HuffPost UK the two parties could agree to some “campaigning cooperation” by keeping activists out of marginal seats they cannot win.
Wilson spoke to HuffPost UK’s Commons People podcast on the eve of the party inflicting a humiliating shock by-election defeat on the Tories in the so-called “blue wall” seat of Chesham and Amersham.
There was a huge 25% swing to the Lib Dems, who won a majority of 8,028 over the second-placed Tories, while Labour was left trailing in fourth.
The result sparked fresh discussion on whether the two sides could agree a progressive alliance - standing down in seats they cannot win to give the other party a clearer run at the Tories.
But a Labour source rejected the idea that the parties could “game the system”.
Wilson also suggested a formal alliance would “backfire”.
But she raised the prospect of the kind of looser cooperation agreed by Tony Blair and Lib Dem leader Paddy Ashdown in the Nineties, where each side would not fight hard in the other’s target seats.
She told Commons People: “For a start, we don’t own any voters so I don’t subscribe to this idea that if a Liberal Democrat stands down in a Conservative/Labour marginal all our votes will suddenly go to the Labour Party and vice versa if they stood down for us.
“Because there’s plenty of soft Conservatives who will vote Liberal Democrat but if we weren’t standing would not vote for the Labour Party.
“So I think what worked incredibly well when you look back to the late 90s was when you had Ashdown and Blair sort of having an agreement that in your marginal seats... take our activists and put them into our own marginal contests and keep them away from those areas that we can’t win.
“And that did not happen in 2019, which is why the Lib Dems... could have picked up a few more seats.
“I think about places like Finchley and Golders Green and Cities of London and Westminster, where we came really close.
“But because they had Labour defectors standing, Momentum purposely sent in hordes of activists to stop the Lib Dems winning - they would rather have Conservative MPs than a Lib Dem MP for their own ideological reasons.
“So I hope there can be some of that sort of obvious campaigning cooperation.
“I don’t think those alliances where we’re standing down for each other necessarily work, and I think they backfire.”
Asked about the prospect of a progressive alliance, a Labour source said: “Look at the number of places where the Lib Dems and the Greens prop up Tory councils to keep Labour out.
“The idea of a progressive alliance is a total myth from people who think you can somehow game the system.”