Theresa May would not have to resign or call a general election if she is defeated in the Commons in a vote on the terms of the Brexit deal this autumn but could instead put the issue back to the people in a referendum, Tony Blair has said.

Speaking at a UK in a Changing Europe event marking a year since Britain notified the EU of its intention to leave, the former Labour prime minister urged Tory MPs to recognise they could keep May in power if she were defeated on the deal.

He said the Conservatives might fare worse at the 2022 election if they backed Brexit in the vote since that would mean Brexit was 100% owned by the Tory party. He predicted that at a 2022 election the Conservatives would face not just the anger of remainers but a lack of gratitude from leavers.

The government is due to put the terms of a deal on Britain’s future trading relationship with the EU to “a meaningful vote” in the autumn. Blair pointed out that May had promised in the Commons on Monday that by the time of this vote MPs would have sufficient detail about the terms of Brexit to come to a judgment, even if much detail was still to be resolved in further talks.

Blair said: “If she is defeated in the Commons she does not need to resign and there does not be an election. She can simply say: ‘OK, I put the deal before parliament; they rejected it. Now it is right the people have the vote and the final say.’

“It is perfectly rational. The country took a decision to leave the EU. The government was mandated to negotiate the deal. It has now negotiated the deal and let us decide whether we like the deal.”

He predicted Labour MPs would vote against the deal, putting the onus on a small group of Tory remain MPs to do the same. It has been frequently argued that Tory MPs dare not defeat May since she would then resign, triggering an election that would be likely to usher in a Labour government led by Jeremy Corbyn.

May has not yet said what she would do if she were defeated in the Commons. The government has instead argued that MPs will have a choice of backing the negotiated deal or leaving the EU on no terms at all.

Labour has said a meaningful vote must include an amendment to the proposed legislation, requiring the government to seek better terms in a further negotiation. Labour’s preferred route is for the issue to be resolved via an election, but Blair argues it is best resolved through a further referendum.

He said that but for a “barrage of propaganda from a rightwing media cartel it would be common sense to say to let us wait to see the terms of the new relationship before we get out of the old one. It is only in the bizarre world that has been created that this is portrayed as a betrayal of the British people.”

Blair said the true test of public opinion would come once the deal was negotiated, but he said already the people had come to recognise that “this a darn sight more complicated than we thought”.