For US citizens, 4 July – Independence Day – is unambiguously an anniversary to cheer and celebrate. As the founder John Adams wrote to his wife Abigail, the day that Congress approved the Declaration of Independence "ought to be solemnized with pomp and parade, with shows, games, sports, guns, bells, bonfires, and illuminations, from one end of this continent to the other, from this time forward forever more." So it is. And as millions of Americans do, I'll join friends and neighbours for a cookout and to watch the fireworks.

But of course, for an English person abroad, resident in the United States, it doesn't mean quite the same. Not that I'm in mourning for the loss of the colonies – in fact, I enjoy the ritual teasing as a "limey" or "Brit", now an immigrant guest in the land that Mad King George lost. Nowadays, I've got my green card, I try to be bilingual in American English, I hold a US driver's licence, I'm even a sustaining member of National Public Radio in two states … in this land of immigrants, I feel as much comfortable belonging as the next person.

But I'm not a citizen. I wasn't brought up to venerate the stars and stripes. And I never learned by heart the text of the Bill of Rights. So, the "illuminations" are great, but inevitably I view them with a certain detachment.

And, in fact, an undertow of envy. While Americans toast their freedom from tyranny every summer, Britons get a royal wedding maybe every other decade, if we're lucky.

It's not as though we of the old country couldn't find a decent anniversary of our own to celebrate. We've got Magna Carta, after all. But can we expect Brits to hold "habeas corpus street parties" for the 800th in 2015?

But if a few rebellious barons bullied some concessions out of King John at Runnymede in 1215, Americans in 1776 liberated themselves from the monarchical principle once and for all. Thomas Paine emigrated to America – and with him went all those wonderfully seditious democratic ideals in Common Sense and the Rights of Man. He left behind a country that would never have a written constitution or formal bill of rights.

And this despite the fact that England did depose a king, in 1648. The year before that, during the parliamentary army's Putney debates, Colonel Thomas Rainsborough anticipated Painite doctrine by more than a century:

"For really I think that the poorest hee that is in England hath a life to live, as the greatest hee; and therefore truly, Sr, I think itt clear, that every Man that is to live under a Government ought first by his own Consent to put himself under that Government; and I do think that the poorest man in England is not at all bound in a strict sense to that Government that he hath not had a voice to put Himself under."

So are the Putney debates remembered as a foundational moment of British democracy, in the way that every grade-schooler in the US knows the Declaration of Independence to be of American democracy? Hardly.

Instead of the United States' great national myth, Britain has a footnote.

And just to get to the end of this grousing: where America's founding fathers safeguarded religious liberty even as they separated church and state, the Church of England – an institution created by another British monarch for entirely self-serving reasons – still packs to this day, as of right, the upper chamber of parliament with its "Lords Spiritual". Since we permitted a royalist putsch, with the restoration of Charles II, Britain ended up with fundamentally conservative constitutional monarchy. And so it took another 250 years of reformers' fights against entrenched privilege for Britain to arrive at universal suffrage, let alone votes for women.

Lord knows, of course, America is far from perfect: it's hard to overlook the abuse of US military power, the nation's vast inequalities, the callous inadequacy of its social insurance, its bought-and-paid-for political system, not to mention its history of slavery in the ante-bellum south … For all that, the United States of America still holds up a corruscating example to the world:

We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.

That may not be a creed to which my mother country will ever wholly subscribe, but because of the American Revolution and Independence, we can all live in hope. Happy fourth.