When I was a boy, my mum used to go to weddings without being invited. It wasn't just her. Lots of people in Middlesbrough did. If you vaguely knew the bride, and the wedding was in your local church, you would slip in at the back to have a look at the dress and stay for the service, and maybe even the photos in the garden afterwards, and then leave discreetly before the reception.

We all like a good wedding. That much was evident from the wide-ranging collection of new nuptial poems which Carol Ann Duffy brought together in The Guardian last week. Even that temple of sophisticated royal wedding sneering had to suspend its wilful disbelief in the face of what the Poet Laureate and her fellows celebrated – the exchange of vows by a young couple in love. It offers a little window on eternity. And everyone is royal on their wedding day.

Still that doesn't fully explain why we boarded a train to London on Thursday. Not much chance of slipping into Westminster Abbey at the back. But we wanted to walk the busy streets beforehand, amid crowds as giddy as a field of horses with the wind blowing into their nostrils. Then afterwards to watch it on the telly with friends near St Paul's before enjoying a street party (inside if wet) and then down to Inner Temple gardens to watch the fly-past.

I wouldn't exactly call myself a monarchist. I managed to resist the lure of the royal edition of Hello! and its coverline "Kate's Last Days as a Single Girl". But I'm certainly not a republican. I am persuaded by a withering two-word argument on that: President Thatcher. Of course we could get a virtuous president. Someone once suggested that Alan Bennett would make a splendid occupant of the office. But I suspect the old Marxist (Groucho, not Karl) principle would come into play with anyone really suitable for the job not wanting to touch it with a barge pole. The default contention is that if you're not a republican you must be a monarchist, but that reckons without the intrinsic woolliness of the English temperament.

Of course the republicans have all the best arguments. Monarchy is offensive to the principle of equality which underpins so many virtues. It colours how we see ourselves in relation to entrenched power, as subjects rather than citizens. It is a potent symbol of the enormous gap between the rich and powerful with the Queen the largest landowner in Britain. It is an affront to democracy, republicans can explode, with high-octane undergraduate debating society indignation.

You wouldn't start from here, as the man in the Irish joke says. But the reality is that here is where we do start, with an anachronistic dispensation which nicely keeps the head of state out of politics and needs no recourse to all that over-intense saluting of the flag they do in the States. It ensures a continuity which encompasses change, as is shown by the way we have clamped down on hereditary peerages with no collateral damage to the monarchy. Yes, it enshrines privilege, but it is privilege with a heightened sense of duty, which is widely acknowledged in the Queen, but is also evident in the impressive work of her son and his Prince's Trust, and is emerging in the personality of Prince William. And, yes, the Queen lives in palaces, but our celebrity culture celebrates conspicuous wealth among a whole class of individuals far less deserving; and at least the Queen has Tupperware on her breakfast table.

The great paradox at the heart of the republican argument, of course, is that 80 per cent of the population have rejected it. How democratic can you get? The only way the high-minded ideologues have of getting round this is to suggest that the public are somehow too stupid to understand the arguments, when in reality they have been understood and found wanting.

"He seems a decent bloke, young William," said my taxi driver as I headed towards the wedding. The ad hominem argument that William is a good chap is, of course, as invalid as the obverse that we should scrap the monarchy when the Queen dies because Charles's eccentricities have rubbed too many people up the wrong way over the years. A strong institution can cope with the occasional dodgy office-holder. Bad kings do not invalidate monarchy any more than bad popes do religion.

But the monarchy offers something more, something intangible. I am not talking about transcendence or the divine right of kings but something which was summed up in the days when Queen Victoria couldn't be bothered turning up for every state opening of parliament and sent her crown instead. It is a reminder of something mysterious at the heart of the British constitution.

Our monarch has a residual power but it's a passive power. Yet its very amorphous existence prevents worse things from rushing into the vacuum. In modern history, constitutional monarchies tend to be on the side of the angels; Hitler, Stalin, Mao and the rest were nurtured in republics. Having a head of state who stands above politics – and who is nominally head of the armed forces, the judiciary and the church – creates a tamper-proof area in the constitution. If you were starting from scratch you would not invent what has evolved. But it is woven into our national identity.

I didn’t know that, aged five, when I went with the rest of my class down to Acklam Road to wave our little paper Union flags at the Queen as she drove swiftly past in a big black car. I only know that she looked out at us, smiled and waved her inexorable slow graceful wave.

In the end, we default to the important things in life. Family, fun and festival. With all the banners and bunting, crowds and carriages, trestle tables, jams, jellies and champagne, we were, as a friend put it, making memories for our children. What they make of it all will be for them to decide.