British MP Priti Patel leaves 10 Downing Street in London. Picture: AP Photo/Frank Augstein

London - British Prime Minister Theresa May is expected to appoint a new aid minister on Thursday following a resignation which has left her with the difficult task of finding the right person to maintain fragile unity in a cabinet divided over Brexit.

On Wednesday, cabinet minister and strong Brexit supporter Priti Patel resigned over undisclosed meetings with Israeli officials, saying her conduct had fallen below the standards required of her post.

That has forced May into her second cabinet reshuffle in a week after former defence minister Michael Fallon resigned in a sexual harassment scandal that has also led to investigations into the conduct of two other ministers including May's deputy.

The instability in her top team adds to what is already a difficult situation for May.

An ill-judged snap election in June cost her party its majority in parliament and has left her authority badly weakened at a time when she is trying to negotiate Britain's departure from the European Union in Brussels and heal deep divisions within her own party.

Sixteen months after Britain narrowly voted to leave the EU in a referendum, opinions are still split over Brexit at every level from voter to minister.

Although May and her cabinet are united in their intention to take Britain out of the EU, her ministerial team is seen as a delicate balancing act between lawmakers who are still identified as 'remainers' or 'leavers' according to how they voted in the referendum.

In replacing Patel, a prominent leaver, May has to try to maintain that balance whilst also placating younger members of the party, many of whom are angry at her mishandling of the snap election campaign and feel they should be given a chance to regenerate the party's support.

Failure to satisfy the party is seen as a risk to May's future as leader. She is reliant on uniting all her lawmakers to pass legislation, including the laws needed to enact Brexit, and if she is unable to do so the Conservative party - historically intolerant of weakened leaders - could seek to replace her.

That would not automatically trigger a fresh national election, however, with many Conservatives fearful that the opposition Labour Party, led by socialist Jeremy Corbyn, could cast them out of power.

Labour performed far better than many had expected in June's election.