Theresa May will have more women in her Cabinet than any previous Conservative Prime Minister, with one of the three big offices of state expected to be filled by a woman.

In contrast to Margaret Thatcher, who chose to be surrounded by an all-male Cabinet for almost her entire time in Downing Street, sources close to Mrs May say that she is determined to put into effect a long held belief that there should be a better gender balance at the top end of the government.

Five women besides Mrs May already hold Cabinet posts – Justine Greening, Nicky Morgan, Amber Rudd, Liz Truss, and Teresa Villiers. Others possibly in line for promotion to the Cabinet include the Works and Pensions minister Priti Patel, who played a prominent role in the Brexit campaign, and the Business minister, Anna Soubry, who backed Remain.

The incoming Prime Minister will also have to consider whether to promote her former rival Andrea Leadsom, to the Cabinet.

The Works and Pensions minister Priti Patel is tipped for promotion to the Cabinet (PA)

A spokeswoman for Mrs May said: "It was Theresa that set up the campaign to elect more female MP's to parliament - and she has always believed that there should be more women in prominent government positions."

Her determination to have a woman in one of the top three ministers means that either the Chancellor George Osborne, or the Foreign Secretary Philip Hammond, or the Commons leader Chris Grayling, who ran Mrs May’s leadership campaign, will have to stand aside.

One of the first appointments Mrs May is expected to make is the Cabinet minister who will have the vital job of handling the Brexit negotiations with the rest of the EU. He or she will head a brand new government department, and yesterday, civil servants were scouring Whitehall looking for a suitable building where it can be housed.

Andrea Leadsom announcing on Monday that she would drop out of the Tory leadership race - she is also a Cabinet contender (EPA)

Her spokeswoman said: “Civil servants have already been charged with finding a building to house the Brexit department - an indication of Theresa’s commitment to get on with delivering the verdict of EU referendum. Brexit means Brexit and we're going to make a success of it.”

Mrs May still has a few hours to wait before she moves in to 10 Downing Street as only the second woman Prime Minister in British history.

Yesterday David Cameron chaired his final Cabinet meeting – the 215th since he became Prime Minister. As it ended, he said presiding over the Cabinet had been “an honour and a pleasure” and praised Theresa May as the right person to take his place. There were tributes to Mr Cameron from Mrs May and the Chancellor, George Osborne, before the traditional banging of the desks.