Theresa May should leave Downing Street by the end of next year to allow a different leader to complete Brexit, a former Cabinet minister says.

Nicky Morgan said the Conservatives should not “miss the opportunity” to bring in a new leader once the shape of the withdrawal agreement is known.

The EU has told Britain that the negotiations must be concluded by the autumn of 2018, to allow a six-month ratification process – something Ms May has apparently agreed to privately.

Most Conservative MPs now expect her to survive in No 10 for the time being, after she eventually struck a deal with the Democratic Unionist Party for support on key votes.

Ms Morgan, who was sacked as Education Secretary by the Prime Minister last summer, said the key date was the likely conclusion of the Brexit talks.

“Once that shape of Brexit is concluded, once those deals are very much on the table, the Conservative Party must not miss the opportunity at that stage to think about who we want to be our future leader,” she said.

Asked, on the BBC’s Newsnight programme, if that meant Ms May should stand down in the autumn of next year, Ms Morgan replied: “That is probably right - certainly one timetable.

“Of course, one of the things the last couple of years has shown is that making predictions about British politics or international politics is incredibly difficult at the moment.

“But I think the Conservative party - having started on the Brexit road - really is going to own the negotiations, is going to own the shape of Brexit.

“That is clearly going to be something that will be, if not the issue of the election, will be something that we will be standing on that record in terms of the party going into the next election.”

Almost all Tory MPs agree that the Prime Minister must fall on her sword before the next general election, scheduled for 2022.

Many think she would be going already if there was an obvious successor, but there is no alternative leader likely to revive the party’s fortunes, they believe.

Both Foreign Secretary Boris Johnson and David Davis, the Brexit Secretary, provoke huge suspicion on the Tory benches and, anyway, have declared their loyalty to the Prime Minister.

The other leading contenders, Chancellor Philip Hammond and Amber Rudd, the Home Secretary, favour a softer Brexit – so would struggle to convince the Tory faithful.

Ms Morgan has been a frequent critic of the Prime Minister on Brexit and grammar schools and is standing to lead the powerful Treasury Committee.