Theresa May has confirmed that MPs would get a final say on whether a backstop solution for the Irish border would ever be put in place, as she attempted to shore up support for her Brexit plan in the first prime minister’s questions of the year.

Speaking before the resumption of the Commons debate on her proposals, which will culminate next Tuesday in a vote postponed from December, May insisted she could reassure MPs about the backstop.

But Jeremy Corbyn, who used all his questions to focus on Brexit, urged May to rule out the possibility of a no-deal departure and said that if she lost next week’s vote she should “let the people have a real say” by calling a general election.

The Labour leader began by saying May had failed to get any further assurances from EU leaders on the backstop, the insurance policy that would prevent a hard Irish border in the event of no permanent trade deal by keeping Northern Ireland under some EU regulations for an interim period.

“Isn’t the PM bringing back exactly the same deal she admitted would be defeated four weeks ago?” he asked.

May responded by saying she had gained new EU assurances with legal status, adding: “These discussions have shown that further clarification on the backstop is possible, and those talks will continue over the next few days.”

She highlighted the government’s new package of methods for Northern Ireland to have a say on the backstop, if it came into effect. The prime minister continued: “We’ve also been looking at how parliament can take a greater role as we take negotiations on to the next stage.

“And so I can tell the house that in the event that our future relationship or alternative arrangements are not ready by the end of 2020, parliament will have a vote on whether to seek to extend the implementation period, or bring the backstop into effect.”

This arrangement had been hinted at before Christmas, but May’s pledge is intended to further assure concerned Tory MPs.

However, Corbyn said May was offering only “window dressing”, and predicted the deal would be voted down. The prime minister, he said, was “recklessly wasting time, holding the country to ransom with the threat of no deal, in a desperate attempt to blackmail MPs to vote for her hopelessly unpopular deal”.

Twice Corbyn asked May if she would discount the idea of no deal, especially after MPs backed an amendment to the finance bill from Labour’s Yvette Cooper to curb some of the government’s tax administration powers in the event of the UK crashing out of the EU.

“Will the prime minister listen to the will of house last night, end this costly charade, and rule out no deal?” the Labour leader asked.

May responded by saying Corbyn was himself ruling out the only deal acceptable to Brussels. “The only way to avoid no deal is to vote for the deal,” she said.

Corbyn lambasted May over her position. He said: “Instead of backing industries in this country in protecting thousands of jobs in manufacturing and service industries, her transport secretary is awarding millions of pounds of contracts to ferry companies with no ferries, to run on routes that don’t exist, and apparently they won’t even be ready by the end of April either.

“This is the degree of incompetence of this government in dealing with the whole question of relations with the EU.”

He continued: “The prime minister has spent the last week begging for warm words from EU leaders, and achieved nothing. Not one single dot or comma has changed.

“So if her deal is defeated next week, as I hope and expect it will, will the prime minister do the right thing and let the people have a real say and call a general election?”

May rejected the idea, and instead mocked Corbyn for what she said were his changing views on many elements of Brexit, such as free movement, the customs union and when to begin the departure process.

She said: “The one thing we know about the right honourable gentleman is that his Brexit policies are the many, not the few.”