The transport secretary, Chris Grayling, has said a change of prime minister was not “on the agenda”, but that a Conservative deal with Democratic Unionists MPs to support the minority government may not be sewn up until after the Queen’s speech next week.

Grayling, who ran Theresa May’s leadership campaign after David Cameron’s resignation last summer, said the Brexit talks, which began in Brussels on Monday, should take priority over a potential leadership contest.

“I don’t think a change of prime minister should be on the agenda, we’ve got to go into the Brexit talks, deliver a good outcome, that’s what she’s committed to and that’s what we want to see happen,” Grayling told BBC Radio 4’s Today programme.

The Queen’s speech outlining May’s legislative agenda has been written despite talks continuing with the DUP, whose support the prime minister will need to secure a majority of votes.

One source said the DUP had agreed to back the document more than a week ago, but that it would be heavily stripped back. However, opposition MPs are preparing a series of amendments, which the DUP or Tory rebels may choose to back or allow to pass.

The DUP has said it will act as a “brace against hard austerity” in its deal with the Conservatives and Labour could put down amendments to torpedo various austerity measures, including the bedroom tax, school cuts and means-testing winter fuel payments for pensioners.

Arlene Foster, the DUP leader, and MP Nigel Dodds arrive at Downing Street for talks with Theresa May last week. Photograph: Jack Taylor/Getty Images

“The talks are still going on, but the one thing I am absolutely certain of is that the DUP don’t want to see another election and Jeremy Corbyn in Downing Street,” Grayling said. “I’m sure we will have a sensible arrangement and they will vote with the government.

“I’m not pessimistic about this, the talks are going on, they are going well, we’ve got some days before we get to a vote on the Queen’s speech. The vote happens many days later.”

Grayling said the Northern Irish party did not want to see “an unstable government undermining our union” and said the party also wanted to see the government prepared for the Brexit negotiations.

Allies of both the Brexit secretary, David Davis, and the foreign secretary, Boris Johnson, denied on Monday night that they were jostling to replace May should her support collapse around the Queen’s speech.

Grayling said the election, where the Conservatives lost their majority, was a “disappointing result” but said the government needed to carry on. ‘We’re dealing with major issues around security, around Brexit. We were by far the largest party. We need to get on with the job,” he said.



“Labour is strutting about like it won the election, we have the shadow chancellor [John McDonnell] calling people to go on to the streets to overthrow the results of a democratic election, which is an extraordinary place to be.”

Grayling, who campaigned for leave during the EU referendum, denied the UK had capitulated over the timetable for the Brexit negotiations. A key UK demand, for parallel talks on a new free trade agreement at the same time negotiators thrash out the multibillion-euro UK divorce settlement, has been ditched.

Previously Davis said the issue would become the “row of the summer” but the chief EU negotiator, Michel Barnier, said Britain was in no position to dictate the timing of the negotiations.

Grayling said the retreat was not symbolic. “Nothing’s agreed until everything’s agreed and we’re actually starting the talks on two areas that are priorities for us,” he said.

“We’ve agreed to talk about the right of EU citizens, which we’ve said all along is a priority for us, right at the start. We’re also talking about the issue of the Irish border, that’s a real priority.

“We are dealing with things right at the top of the list, we want to give certainty to those EU citizens in the UK, we want to deal with the Irish question. We want an arrangement to allow us to tie up the mechanics of leaving the EU, we want to have a sensible trading partnership and we want to give businesses certainty that there isn’t going to be a cliff-edge.”

May will travel to Brussels this week for the European council meeting, where she is set to unveil the terms of a new British offer to guarantee the rights of EU citizens living in Britain.

The full details of the offer will be published in a paper next Monday, but some in the EU have expressed concerns they will not match the full spectrum of rights that EU citizens currently enjoy living in Britain.