'Justine Greening has called for a second referendum, labelling the prime minister's Brexit deal a "fudge".
Writing in the Times, the former education secretary described Theresa May's proposals as "the worst of both worlds".
The final decision should be given back to the people and out of "deadlocked politicians" hands, Ms Greening said.
She states there are three options: the PM's deal, staying in the EU or a clean break from Europe with no deal.
Ms Greening, who resigned after the cabinet reshuffle in January, said the referendum should offer a first and second preference vote so that a consensus can be reached.
Speaking on BBC Radio 4's Today programme, Ms Greening said the government's proposals were a "genuine clever attempt at a compromise that could work" but "suits no-one".
The MP for Putney said: "The reality is Parliament is now stalemated. Whatever the proposal on the table, there will be MPs who vote it down. But Britain needs to find a route forward."'
Read more: Justine Greening calls for second Brexit referendum