Is Boris Johnson allowed to pick the next Archbishop of Canterbury?

A few weeks ago, Prime Minister Boris Johnson was shirty with me when I asked him whether he was now a practising Roman Catholic, having recently been married to Carrie Symonds at Westminster Cathedral. His answer was ‘I don’t discuss these deep issues. Certainly not with you.’  

The question may be ‘deep’, as he says, but it is also – as a senior minister has reminded me – an intensely practical one and relevant to his duties as Prime Minister.