Now that Britain’s latest prime minister has gone through the ritual of ‘kissing hands’ with the monarch – these days, a small bow tends to be the preferred option instead – there will be a great deal of whispering in Buckingham Palace as to what the relationship between the King and his latest first minister is going to be like. The first photograph of the two shaking hands showed the new prime minister smiling broadly and enthusiastically, and Charles, understandably, seeming rather more restrained. This may be a preview of things to come. Since Charles inherited the throne a shade under four years ago, Burnham will be his fourth prime minister – a fairly rapid number in what has been a decidedly unsettled time – and while everyone must hope that the relationship between the two is amicable and productive, there are some potential pitfalls ahead.

Burnham’s USP, such as it is, is stripping away a great deal of formality from the office of PM. This has promised to manifest itself in such initiatives as not wearing a suit and tie except when wholly obligatory, his refusing to leave his family home in Manchester and adopting a more relaxed, accessible style. It is not beyond imagination that he might seek to embrace King Charles, rather than bow to him. And while Charles has been responsible for some limited attempts to modernise the monarchy, he is still a great believer in the formal trappings of the institution and is likely to react poorly to Burnham-led mateyness.

The King has not had the easiest relationship with his previous prime ministers – Old Wykehamist Sunak aside, who he got on well with by all accounts – and while Charles initially regarded Starmer as a serious man who was in Downing Street to do a job of work, there was an inevitable personality mismatch between a poetic monarch who is a keen aficionado of the arts and culture and a premier who governed and lived alike in the most boilerplate of prose. There is a chance that the king will warm to the first English literature graduate who has ever entered 10 Downing Street, and while his own tastes may not quite include Burnham’s favourite poets, Philip Larkin and Tony Harrison, there is the opportunity to find shared intellectual interests.

It remains to be seen what Charles will make of Burnham’s self-proclaimed Manchesterism, or what the personal relationship between the one-time King of the North and bona fide king turns into. His mother, after all, became very close to Harold Wilson, another northerner who liked to turn his back on airs and graces, and it might be that Charles finds Burnham refreshing and unpretentious, even if he chafes at his lack of noblesse oblige. Or, alternatively, he will find the football and music-loving PM too far out of his element to be able to have anything other than the most limited of dealings with.

The two men are not believed to have had any significant interactions before now, although Burnham was (perhaps unfairly) mocked in June 2009 for sending Charles a letter thanking him for his good wishes on being appointed health secretary and ending it with ‘I have the honour to remain, Sir, Your Royal Highness’s most humble and obedient servant.’ While this was widely viewed as unnecessarily obsequious, it was also following standard practice as set out in Debrett’s, that bible of etiquette.

If Burnham approaches his monarch in such a similarly toadying fashion, then the relationship is unlikely to progress, just as the King is not going to appreciate back-slapping mateyness and being referred to, over-familiarly, by his first name. However, if the new prime minister finds a balance between his natural warmth, friendliness and respect, listens to any advice that the King has for him and doesn’t chew his ear off with recommendations for obscure Manchester bands, there is every chance that the two men could find a decent rapport. But if Burnham – the first Catholic prime minister that the defender of the faith has dealt with – treats the monarch as another representative of the southern metropolitan elite that he clearly despises, then matters are going to go very badly, very quickly. All will become clear before too long.