A major sticking point in talks between Britain's government and opposition Labour Party is the lack of any guarantee that a successor to Prime Minister Theresa May would deliver on any Brexit agreement, Labour's trade policy chief said Sunday.

May, who has offered to quit if lawmakers accept her Brexit deal, opened cross-party talks with Jeremy Corbyn's Labour Party more than a month ago after Parliament rejected her European Union withdrawal deal three times.

Barry Gardiner told Sky News: "We don't know at this stage even if we could negotiate a deal, what we don't know is whether the successor to Theresa May would actually deliver on it and that's one of the big sticking points that we have."

His comments came as prisons minister Robert Buckland said the same day that May does not need to spell out a timetable for her departure, adding the leader had already announced she would leave office after the first phase of Brexit.

May is under pressure to detail when she will leave office from angry Conservative lawmakers who want a new leader to try to improve the party's fortunes.

"The prime minister's said that she is going to go once the first phase of Brexit has been delivered," Buckland told Sky News, adding that meant after the deal agreed with the EU in November was ratified by Parliament.

"If that can be done quickly, then we have that timetable set out already. I don't think she needs to say any more about that. What we need to do is to get on with the job," he said, adding that the deal could be passed in the next few months.