The Cabinet remains deeply divided over Brexit policy

Both of the women were supporters of Brexit.

But this does not even begin to resolve the very serious problems that the prime minister faces when it comes to implementing Brexit.

She has still not given a clear picture of the sort of Brexit that the UK will seek to have, because she cannot do so without fear of splitting her government.

More Conservative MPs in 2016 supported staying in the European Union than supported leaving it, although the divide was close to 50:50. The larger number of Remain Tory MPs was partly due to the fact that the then prime minister and most of his key ministers campaigned to stay in the EU.

Now an overwhelming majority of Conservative MPs believe that Brexit must happen because it is the will of the country.

But beyond that there is a huge range of views as to what shape Brexit should take, in particular with regard to the UK’s relationship to the single market.

If the relationship is too close, and the European Court of Justice still has significant jurisdiction over the UK, Brexiteers could cause havoc for the PM.

If the split is too great, the Remainers could do the same.

On both sides of this bitter divide there are some Tories who feel more strongly about the issue than they feel loyalty to their party. They could vote against the government in key votes or leave the Conservatives altogether.

Meanwhile, the sex scandal could yet lead to departures from Westminster and by-elections, triggering the fall of Mrs May, and possibly a general election.

Labour remains vague with regard to Brexit, partly because its real goal is how to secure such an election.

This is a highly unstable political period in London. Mrs May’s room for manoeuvre is minimal.