Ms Allen predicted the next election would again result in no party winning a majority, which might see the Remain-backing alliance holding the balance of power.
“I think we would find ourselves most likely in a hung parliament again,” Ms Allen added.
“That’s why we’ve been preparing for this Unite to Remain initiative and why I’ve stayed independent for as long as I have – because it is so important.
“It would mean, if as successful as I believe it could be, we could hold the balance of power keeping both a Jeremy Corbyn-majority government and a Boris Johnson or Nigel Farage, let’s be fair – the Brexit Party have candidates too – we would keep both ideological fringes out of majority power.
“And then the dynamics in the House of Commons could shift tremendously.”
Ms Allen is the fourth former Tory MP – joining Sarah Wollaston, Phillip Lee and Sam Gyimah – to join the Liberal Democrats in recent months.
Ex-Labour MPs Chuka Umunna, Luciana Berger and Angela Smith are also among the Lib Dems’ now 19 MPs.