Sexual intercourse may not have begun in 1963, but politicians' sex scandals as we know them now, arguably did.

Fifty years ago tomorrow, John Profumo, secretary of state for war in Harold Macmillan's government, made his fateful statement to Parliament claiming there was nothing improper in his relationship with call girl Christine Keeler. Less than three months later he was forced to resign in disgrace, admitting he had misled MPs.

Since then, feeling let down by parliamentarians has become a familiar experience for British voters. The press had traditionally held back from exposing the peccadilloes of ministers, but the Profumo affair, with its allegations of a possible security breach due to Keeler's affair with a Soviet naval attache, opened the door on MPs' private lives and made a succession of hapless MPs and ministers household names for all the wrong reasons, exposing some to the charge of hypocrisy (remember Back to Basics?). Alongside the sex scandals have come revelations of sleaze and venality, from "cash for questions" under John Major's government to the MPs' expenses scandal in 2009.

It's hardly surprising, then, you might say, that a new survey warns of a deep crisis of confidence among British voters in their parliamentarians, a crisis that has been building for decades. The Economist Intelligence Unit's survey of the state of democracy across 167 countries has found that in the UK "trust in government, parliament and politicians is at an all-time low" and highlights a broader, deeper crisis caused by the recent phenomenon of institutions like the media, churches, banks and the police, falling from grace one after the other like so many dominoes. In a doom-laden analysis, it points a bleak picture of "a seemingly unstoppable breakdown of authority and trust" in the British body politic.

Certainly there is work to be done to rebuild public trust, particularly in parliament, banks and the media, but we're not doomed, not quite yet. Inevitably when a scandal breaks, a sense of perspective is one of the casualties; the MPs who aren't fiddling their expenses on a grand scale and the police officers who aren't selling information – the overwhelming majority – get forgotten amid the hail of condemnation.

In the EIU survey, the UK comes out 16th out 167 countries worldwide for the health of its democracy, not perfect, but hardly disastrous. For the haughty Mother of Parliaments, it is no doubt annoying to be upstaged by former colonies New Zealand and Canada (in fifth and eighth places), but it hardly signals a terminal "crisis". The very idea that British people might be experiencing a dangerous breakdown of trust in the establishment must seem laughable from the vantage point of Syria (164th place), Iran (158th) or Zimbabwe (148th). The exposure of scandal by a free press is not a sign of democratic failings, but a sign that democracy is working as it should (think of the MPs' expenses' affair). Democracy is a process of constant, slow and painstaking reform with no perfect nirvana at the end of it. Holding public institutions to account and pressuring them to do better is its essential feature; unfortunately, expecting them to be perfect is a mug's game.

As for low voter turnout in British elections, so often held up as proof of voters' lack of trust, it is more complicated than that. When people take civil liberties, a free press, a corruption-free police service and transparent politics for granted, they can afford to stop voting. When they know the meaning of oppression from first-hand experience, on the other hand, they will queue for days to cast their ballot. Just ask the people of Tunisia.

Public scandals inevitably deepen cynicism among voters but in a funny sort of way, they are a sign of a democracy in good health.