The source added that, if a Tory coalition was formed, the Lib-Dems could see further seats lost.

“Labour are in power in this city and will probably increase their majority.

“The argument against the Lib-Dems used to be that it was a wasted vote. When it does not matter to vote for us any more, they may start going home to the Conservatives, so wards like Childwall and Woolton, which used to be rock-solid Tory seats, could swing back to them.”

Analysis of the local election results shows that in the wards the Lib-Dems won, the average winning share of the vote was 43.78%.

But, where Labour won, the average was 62.30%.

Cllr Bradley – who has faced calls to resign from both former education executive member Paul Clein and Cllr Kemp – did not respond to the Daily Post’s enquiries yesterday.

Cllr Clein said he had seen the letter, adding: “I’m a Lib-Dem, I have no brief either for the Labour party or the Conservatives and I campaign against both.”

He added that “if we did come to some kind of arrangement with the Conservatives, I would not be too happy, but there’s a need for stability.

“I think if the Lib-Dems did have some sort of arrangement with the Conservatives at national level, I think you would see some of the more extreme elements of the policy platform not included.

“From that point of view, it may be a good thing for the city, not a bad thing.”

Cllr Kemp, who was last night in London to meet with negotiators, added: “First of all, we have to consider not just Liverpool but the country.

“What the negotiating team is doing is maximising the input into any parliament of what we put in our manifesto, big things like electoral reform, the budget deficit and civil liberties.”

He added: “Whether I like it or not, and I clearly don’t, the Tories have got more seats than anyone else. Whether or not some voters will like it or not, only time will tell, because it will depend on what we can achieve.”