The leader of the Change UK party, said she threatened to quit after an internal party row over whether to endorse the Liberal Democrats during the EU elections.
Heidi Allen wanted Remain supporters to vote tactically for the Lib Dems outside of London and the South East, but was overruled.
She told Channel 4 News: ‘Had it been left to me, I would have absolutely advised tactical voting. [Group members] didn’t want to go that way, but it is something that still troubles me.
‘I have no doubt that the British public will look at the tactical voting websites out there and make their own decisions.’
Miss Allen – MP for South Cambridgeshire – was one of three Tory MPs to resign their party’s whip to join eight Labour defectors to form Change UK.
When pressed on whether she had threatened to resign over the matter, she said: ‘I did.’
She added: ‘Putting all the votes in one direction doesn’t always create the result that you want.
‘If the next party further down in the polls isn’t still big enough to win a seat, you can end up… giving more votes to the Brexit parties. Ultimately, do I think we have reached an acceptable balance point? Yes, I do.’
It comes as pressure is intensifying on Theresa May to resign after Commons Leader Andrea Leadsom quit the Cabinet over the Prime Minister’s Brexit plan.
Mrs Leadsom resigned with a “heavy heart”, saying she no longer believes the Government’s approach will deliver on the referendum result to leave the European Union.
The PM, writing in reply, disagreed with the ex-minister’s assessment, but said she was sorry to lose someone of Mrs Leadsom’s “passion, drive and sincerity”.
“I do not agree with you that the deal which we have negotiated with the European Union means that the United Kingdom will not become a sovereign country,” Mrs May said.
She went on to say she agreed a second referendum would be divisive, but said the Government was not proposing to hold one.
Mrs Leadsom acknowledged her resignation came on the eve of the European elections, but said she felt she could not announce the Withdrawal Agreement Bill (WAB) in Thursday’s Business Statement containing “new elements that I fundamentally oppose”.
“I fully respect the integrity, resolution and determination that you have shown during your time as Prime Minister,” she wrote in a letter to the PM.
“No one has wanted you to succeed more than I have, but I do now urge you to make the right decisions in the interests of the country, this Government and our party.”
Listing her reasons for resigning, Mrs Leadsom said she did not believe that the UK will be “truly sovereign” through the deal proposed, and said a second referendum would be “dangerously divisive”.
She added that there had been “such a breakdown of government processes” that recent Brexit-related legislative proposals have not been “properly scrutinised or approved by Cabinet members”.
And she said: “The tolerance to those in Cabinet who have advocated policies contrary to the Government’s position has led to a complete breakdown of collective responsibility.”
Mrs Leadsom was one of a number of Brexit-supporting colleagues in the so-called Pizza Club who were absent for the start of Prime Minister’s Questions on Wednesday.
In a dramatic night in Westminster, her resignation came as pressure mounted on Mrs May to quit as the backlash over her last-ditch effort to get a Brexit deal through heightened.