LONDON — In a foretaste of the fresh turbulence about to grip British politics, the chancellor Philip Hammond said on Sunday that he would resign if, as expected, Boris Johnson becomes prime minister this week.
Mr. Hammond, who as finance chief is one of the leading figures in Prime Minister Theresa May’s cabinet, made his announcement in an interview with the BBC when asked whether he expected to be fired this week.
“No, I’m sure I am not going to be sacked, because I am going to resign before we get to that point,” Mr. Hammond said, adding that he expected to step down on Wednesday, the day Mrs. May is scheduled to be replaced either by Mr. Johnson, the former foreign secretary, or by Jeremy Hunt, the current foreign secretary.
The manner of Mr. Hammond’s announcement was more surprising than its content, because Mr. Johnson is likely to demand from all members of his new cabinet a pledge to support, if necessary, a departure from the European Union without any agreement on the deadline, Oct. 31.
A prominent opponent of such a move, Mr. Hammond is not popular among hard-line Brexit supporters, and neither is the government department he leads, the Treasury, because of its warnings about the economic impact of a rupture with the bloc.
Mr. Hammond’s statement is a reminder of the level of opposition that Mr. Johnson’s uncompromising approach to Brexit is likely to encounter with lawmakers, even within his own Conservative Party, and of the constraints he will face.
Other cabinet ministers are expected to step down, too, rather than sign up to a promise to pursue an exit without an agreement — a move that analysts warn would be disruptive and highly damaging to the economy.
That group includes Greg Clark, the business secretary, and David Gauke, the justice secretary.
Mr. Gauke told The Sunday Times of London that, if a no-deal Brexit were pursued by Mr. Johnson, then his own resignation would be the “appropriate thing” to do.
“If the test of loyalty to stay in the cabinet is a commitment to support no deal on 31 October — which, to be fair to him, Boris has consistently said — then that’s not something I’m prepared to sign up to,” Mr. Gauke said.
The newspaper also reported that some Conservative lawmakers could defect to the centrist and pro-European Liberal Democrats, making the math in Parliament even more challenging for Mr. Johnson, who will inherit a working majority of roughly five.
The transition of power from Mrs. May to either Mr. Johnson or Mr. Hunt, who are in a runoff to become the Conservative Party’s new leader, comes as Britain faces a difficult diplomatic standoff with Iran over the seizure of a British-owned oil tanker on Friday.
In his BBC interview, Mr. Hammond said it was important that the next prime minister and his chancellor be “closely aligned” on Brexit policy.
He added that his future “might be more complicated” if Mr. Hunt were to win the Conservative leadership contest — though whether he would be allowed to keep his position as chancellor in that case is far from clear.
But Mr. Hammond noted that all the polling suggested that Mr. Johnson would win a majority of votes from party members who will elect the new leader.
“That is what is likely to happen, and I’m making my plans accordingly,” Mr. Hammond said, adding that he would wait until the result of the leadership contest, which will be announced on Tuesday, and remain chancellor at least until Wednesday.
On Sunday, the Irish foreign minister, Simon Coveney, said that the European Union would want to engage with the new British prime minister, but he rejected Mr. Johnson’s ideas for scrapping the withdrawal agreement that the bloc negotiated with Mrs. May.
The British Parliament has rejected those plans three times, and Mr. Johnson has refused to rule out suspending the legislature to get past the Oct. 31 deadline and in that way take the country out of the bloc by default.
Last week, lawmakers including Mr. Hammond were among senior Conservative lawmakers who abstained on a motion that was intended to make it harder for Mr. Johnson to bypass Parliament to leave the European Union without an agreement. That measure passed by 41 votes.
Nicknamed “spreadsheet Phil” because of his attention to detail and perceived lack of charisma, Mr. Hammond has been Mrs. May’s chancellor since 2016, when she took power. Relations between the two have become strained recently, however, as she has sought to secure funding for projects to secure some sort of political legacy for her troubled premiership.