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.Because under the British constitution:

1. The Prime Minister’s appointments secretary has an advisory role in the appointment of all bishops

2. The chair of the commission that nominates an archbishop is chaired by a lay person selected by the prime minister

3. The PM eventually picks a bishop or archbishop from a short list of two (though except in exceptional circumstances, the PM accepts the preferred candidate of the commission).

In other words, the PM and the PM’s office is intimately involved in deciding who runs the Church of England, and – as a member of the cabinet told me – this would not be appropriate or possible if the PM is a practising Roman Catholic.

In fact, as I understand it, there is a contingency plan in the event any PM is not Church of England, for these duties to transfer to the Lord Chancellor (whose current encumbent, Robert Buckland, is steeped in the established church).So at some point, Boris Johnson will surely have to disclose whether he tied the knot in a Roman Catholic cathedral with a special dispensation from Rome, whether in fact what happened in the cathedral was a blessing rather than formal marriage, or whether in fact he is the first avowedly Roman Catholic head of the British government.

When I asked the PM about it at the G7 in Cornwall, he implied his religion was a private matter.

As it happens, I am an agnostic or secular Jew, who has immense respect for people of faith. And in normal circumstances, I would never put pressure on someone to talk about religion if this were to make them uncomfortable.

But the PM is not any old private individual. He or she is intimately involved in the governance of the Church of England. So this question of conscience is a public interest question.

I asked a senior official what the PM would lose by standing aside from any involvement in the Church of England.He pointed out that the PM’s great obsession is in appointing Brexiters and Johnsonians to all the important public offices, to sweep away what he sees as the toxic hegemony of the Blairites and the reviled liberal metropolitan elite.We’ve seen that with controversies over appointments to chair the BBC and the media regulator Ofcom (though I am not sure how the appointment of the arch Remainer and liberal metropolitan George Osborne to chair the British Museum is consistent with that rubric, though maybe his Toryness is enough).

The relevant point is that the current Archbishop of Canterbury, Justin Welby, has never knowingly held back from criticising ministers or the Tory government when he sees them as trampling on the poorest and weakest.Within what used to be known as the Establishment, Welby has been a rare public critic of Mr Johnson, and in an interview in the Sunday Times in October 2019 he appeared to admonish Mr Johnson for using inflammatory language to foment dangerous divisions, especially over Brexit.

So my mandarin source wonders whether Boris Johnson’s seeming reluctance to recuse himself from any influence over the choice of the bishops and of Welby’s successor stems from an unwillingness to abandon a personal role in the culture wars, as they pertain to the Church of England.

Or to put it another way, he speculates that Mr Johnson would like to have a voice in preventing Welby being replaced with someone he would see as another irksome lefty.

All of which is intriguing, except that it founders on one simple point: Mr Johnson is either a Roman Catholic or he is not. As prime minister, ambiguity isn’t possible, he can’t be both Roman Catholic and Church of England; on this, he can’t have his cake and eat it, because under the 1829 Roman Catholic Relief Act a PM who is Roman Catholic cannot advise the monarch on the appointment of bishops.

So presumably before another bishop vacancy is to be filled, he’ll either have to abolish the 1829 act – though it would be eccentric if a PM who isn’t Church of England were to advise on Church of England appointments – or profess his avowed faith in public.

Boris Johnson may not think that’s fair, but hundreds of years of turbulent British history make it very hard for any PM to insist that his or her faith is a purely private matter.