Boris Johnson has said that all Tory parliamentary candidates have committed to vote for his Brexit deal if he wins a majority at the general election.

In an interview with the Sunday Telegraph, the prime minister said this pledge means that voters can be “100%” certain that a Conservative government will “unblock” parliament and deliver Brexit.

Last month, Johnson’s withdrawal agreement bill was approved in principle at its first hurdle when MPs voted 329 to 299 for it, but the blow came when they rejected the hasty timetable by 322 to 308. It put paid to his promise – “no ifs, no buts” – to take the UK out of the EU by 31 October.

Johnson told the newspaper: “All 635 Conservative candidates standing at this election – every single one of them – has pledged to me that if elected they will vote in parliament to pass my Brexit deal so we can end the uncertainty and finally leave the EU.

“I am offering a pact with the people: if you vote Conservative you can be 100% sure a majority Conservative government will unblock parliament and get Brexit done.”

The newspaper also reported the prime minister has confirmed that he is postponing a plan to increase the threshold at which people start to pay the 40p tax rate.

“We do want to reduce the burden of taxation,” he said. “That’s very much our ambition but we won’t do that until we have done more to lift the burden, particularly on people on low incomes.

“So the particular measure that you describe is something that remains an ambition but we won’t do it until we have done more for people on low incomes.”