There are three ways to respond when the going gets tough: head in the sand, try to sort things out, or suddenly get very busy elsewhere. Which perhaps explains why David Cameron has been focusing so much on "abroad" recently, and I don't just mean his bargain break in Spain.

With his government's two flagship policies in crisis, Cameron has decided to apologise for Britain's role in world conflicts. This will do nothing to sort out the chaos of tuition fees – with most universities now declaring themselves the exception and charging the full whack of £9,000. Nor will it help the unnecessary revolution in the NHS, which has at least been "paused" in the light of howls of fury from the professionals.

Yes, the British are pulling in their belts and bracing themselves for some sparse years ahead – except apparently abroad, where the union flag flutters high as ever. Look at the pilots over Libya, the troops in Afghanistan, the diplomats and the aid workers. From the mountains to the deserts, the demands seem endless for Britain to "step in", and today's politicians clearly enjoy the international spotlight just as much as yesterday's. Yet the mismatch between the bulldog's growl and the reality of its kennel has never been greater.

It's often said that prime ministers arrive determined to push through a domestic agenda until they eventually get distracted by the glamour of overseas crises. This happened with Margaret Thatcher three years in, when the Falklands crisis was forced on her; and with Tony Blair as the Balkans blazed, long before Iraq. Blair's focus on domestic policy never really returned; had it done so, maybe he would have wrestled control back from his chancellor.

Cameron's whirlwind romance with the international spotlight has happened even faster. He arrived as a man bent on dealing with the deficit and promising his "big society" as a cure for socialist statism. Yet the crises at home now include not only health and higher education, but the cost of petrol, problems over pension reform and now, we hear, a row with the Lib Dems over banking reform. You would think, given all this, that the prime minister had no time for anything else. Far from it. The bugle has sounded, calling him to high-level talks in London; summits across Europe; confabulations with Barack and Hillary; more emergency statements in the Commons, with furrowed brows and much backbench applause. I am not particularly blaming Cameron. We have seen it all before; remember how Blair suddenly ascended into heaven on Blairforce One and spent most of his time pop-eyed with history-making grandeur?

Part of the problem, of course, is that it is simply more exciting to make peace and war, than to struggle with the details of welfare reform or how to cut civil service budgets without a vote-destroying loss of service. It's more exciting for the ministers but also for their advisers and for the media pack watching; bangs and clouds of smoke seem to sell front pages and news bulletins too.

Yet I would argue that something happens in particular to British prime ministers, in the here and now, which is a problem and is correctable. Few other countries, bar France, have an equivalently grand post-imperial, military-state set up. I don't mean the buildings, though these play their part, but more the whole panoply of mysterious secret service chiefs, chiefs of staff, UN security council membership, nuclear buttons and telephone hotlines. You want to speak to the White House? No problem. You need to visit our boys? Helicopters and jets are waiting. For a young politician who had only had a job as a PR man before Westminster it must have been particularly head-turning.

And once upon a time it might even have been reasonable, as Britain continued to gently adjust to new realities. But we have a big debt, dwindling military capabilities and far bigger problems to confront as a country. We don't know how we are going to pay our way in the world any more. We are still unsure of how, if at all, we fit into the rest of the European project. It is no longer appropriate that it is Britain who, when some part of the world goes up in smoke, rides first toward the sound of gunfire.

We should do our bit, but no more. We should learn our lesson after Iraq. Why should richer, bigger Germany do so little in Afghanistan? Why was Libya not an Italian problem before it was a British one? Now that India and Brazil bulk so large on the world stage, why aren't these two democracies doing more for the democratic cause?

If our gung-ho attitude to foreign intervention is a displacement activity, distracting us from economic and industrial decline, then we need to wake up. If we do it because we think it makes a little of America's lustre rub off on its most loyal ally, we should take a good look in the mirror and around the world. If we carry on because "that's what we're good at" (fighting) then we need to ask ourselves if this is really the national specialism we want, given how many people it kills and maims, how much anger it causes abroad and how we do it for no payment at all.

It's time, after Cameron's apology, to turn our backs on our imperial-military past and become a different kind of country again – harder working, better educated, readier to bring aid and medicine than warplanes. It would be a hard adjustment for parts of the London establishment but it would be better for our long-term security. And there is an obvious way to begin.

Get rid of Trident. Junk any kind of replacement, and do it now. We would save ourselves anything between £25bn and £35bn, which would be pretty useful. We could spend it on better technical education and help for start-ups; but the money isn't really the point. Abandoning our own contribution to possible Armageddon means abandoning our membership of the nuclear club, or what diplomats rather bizarrely tend to call "the top table". Do we really want to eat there any more? The conversation's terrible and the menu is monstrous.

It would feel quite brave. It would be final. It would mean politicians voluntarily renouncing the stilts that nuclear missiles give them at international gatherings. It would unwind part of our closeness to the US military and intelligence world. Most important of all, it would be a big national statement, which said simply: "Britain is changing direction, and this time we mean it."

And then, having discarded our foreign delusions of grandeur, there's a domestic agenda to focus on – the health service, tuition fees and the rest.