You may think it unsurprising that a beneficed clergyman of the Church of England could find a reason to come out in favour of the monarchy. The sovereign is of course the church’s supreme governor, to whose majesty I swore at my installation as vicar of Finedon that I would be faithful and bear true allegiance, according to law; so help me God.

But many of us are not monarchists, emphatically not, including bishops, one of whom was suspended for a while after he made disparaging comments about the marriage of Kate Middleton and Prince William. Monarchies are human institutions, they argue, that enshrine inequality, and deny the equal dignity of all people made in the image of God. Such a view has a long and honourable history, and people have chosen to die rather than abjure it. When I was first ordained, it was my view.

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It is not now. My conversion was forced on me not by a blinding epiphany, or an invitation to a garden party, or a compelling argument. I was turned by Princess Anne. She was patron of an appeal I was involved with and came to support a fundraising event. Her presence turned out the entire town and the appeal, which had struggled to get going, received such a boost that we were able to reach our target.

Her support made the difference, and I was obliged to reconsider at least the usefulness of the monarchy. It has a reach that is unparalleled; it can wake up dormant goodness and generosity. But then, so does Comic Relief and Children in Need; what is special about the monarchy? Why should we pay to keep the royals in their palaces and castles, attended by liveried servants? The precise figures are disputed, but it seems that the monarchy brings in more than it costs, so the economic argument against it is not persuasive to me. But why support an institution that enshrines at its heart privilege, status, wealth, deference and class?

I would feel the power of this more forcefully if there were better evidence of societies that organised themselves effectively without hierarchy. And if we are going to have a hierarchy then I would rather have one that instils in those at its apex robust ideals of service and duty than ones that sustain ridiculous oligarchs in golf resorts.

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I am not in favour of hierarchies that grant privileges to members who fail to uphold those values – there are plenty of those – but the monarchy is really the Queen, who is of unimpeachable integrity and the longest serving head of state in the world, and who never puts a foot wrong. She is steady, dutiful; an icon and inspiration to all. Very few would dispute that the Queen’s personal qualities are remarkable, but I am not a monarchist for that reason, any more than she would be.

If I had to argue for the monarchy, I’d rely on two principal reasons. The first is that it is, to use a word in vogue, relatable. The historic identities of our countries, their polities and cultures, are encoded in the lives of these people, and in their stories we locate our own. I was recently at Westminster Abbey for evensong, surrounded by the Queen’s predecessors, from Edward the Confessor to George II, and side by side with her namesake, the first Elizabeth, and Elizabeth’s cousin and victim, Mary Queen of Scots – a reconciliation achieved in marble that flesh could not manage. This marmoreal pageant, where the personal and the institutional meet, is a narrative that was there before we were, and will be there after we have gone. It transcends the ideological commitments and political passions of the moment, and provides a context that reminds us we have a common interest, a common identity, and that it is accessible to all.

The second is the advantage of having a head of state who is not a party political creature. I find it immensely reassuring that the Queen is neither Conservative (rather than a conservative) nor Labour when she deals with prime ministers who are as opportunistic as viruses. Her steadiness, that most important quality, is unaffected by the tides of political fortune or the temptations of political activism.

I was watching the riots in Barcelona a few months ago and remember years before having coffee there with the veteran Catalan nationalist Jordi Carbonell, who was exiled to England during Franco’s regime. He said: “You don’t know how lucky you are to live somewhere where party interest and national interest are not perceived as the same thing.” I think he was right, and that in an era of growing anxiety, and even menace, the monarchy here, like other monarchies in other places, could be our best defence against the rise of tyrants.

• The Rev Richard Coles is parish priest of St Mary the Virgin in Finedon, Northamptonshire, and co-presenter of BBC Radio 4’s Saturday Live