Sir John Major has called for MPs to be allowed to have a free vote on a series of options to solve the unfolding Brexit crisis, saying he feared millions will be hurt if Britain leaves the EU with the wrong deal or none at all.

The former prime minister called on Theresa May to stage a series of “indicative” votes in parliament to establish whether any proposals could command a majority.

“The prime minister … fought for her deal, she got a deal, she argued valiantly for it, but the House of Commons killed it and killed it comprehensively,” he told BBC Radio 4’s Today programme. “So her deal is dead and I don’t honestly think that tinkering with it is going to make very much difference, if any difference at all.

“And so the prime minister still needs a deal. If she can’t deliver one that parliament accepts, then she needs to become a facilitator, a mediator, to find out what parliament will accept.” Ideally the party would permit a free vote, he said, “so that we can get an honest representation of parliament”.

He said: “It’s the only way to get an absolutely honest answer from members of parliament, and if it is a free vote, it removes the danger of resignations from government or the opposition front bench because they disagree with their leader’s policy.”

He added: “This is such a unique issue, I think it would be an act of statesmanship by the party leaders to say: ‘Because of the very strong opinions on either side, we are going to lift the party whips so parliament and the country can get a genuine view of what it is members of parliament most think would be best for our country or, perhaps, least bad for our country.’ It is a unique way of doing it, but I think it is justified.”

In 1971, the then prime minister, Edward Heath, offered Tory MPs a free vote on whether to join the European Economic Community in order to help solve division.

Major also said that if the cabinet or parliament could not find a solution, then the other option was to have a second referendum.

Major’s comments come after he wrote an article last week in which he said revoking article 50, which gave the country two years to leave the EU after it was triggered in 2017, had become the “only sensible course”.

On Saturday, Major told BBC’s Today programme: “I’m no longer in politics; I have no axe to grind. I’m not part of the remain campaign, and I’m certainly not part of the leave campaign. I can look at it quite dispassionately … and I will tell you my fear. My fear is that millions of people who do not deserve to be hurt, both businesses and individuals and families and young people with their prospects, are going to be hurt.

“And if I have to eat past words because I now realise that is the case, I will make a meal of them every single day, because it is the future, and those people, I believe, are the primary responsibility of parliament, and if parliament does not address that responsibility, then parliament will, in my view, have failed in its duty.”

Later in the programme, the former Brexit minister and Leave campaigner Suella Braverman, who resigned from government in protest at May’s deal, dismissed Major’s comments, describing them as “remainer elite views”. “Thank you Sir John, but no thanks,” she said.