David Cameron was wrong. He thought that he would have a very brief honeymoon period, if any at all. Yet now, a lunar month after he kissed hands, the honeymoon shows no signs of ending. This is evidence of a disjunction between the political class and the general public. Many of those who follow politics closely find the coalition bewildering and are suspicious of it. Most of the public rather like it. A lot of voters believe that politicians ought to cooperate, and the impression that this is happening is reinforced by the temporary absence of an effective opposition, as Labour devotes all its energies to choosing a new leader.

Moreover, the coalition is working surprisingly well. This is due to a blend of leadership, technicalities and personalities. On Friday 7 May, David Cameron woke up and knew what was needed: a strong government. He also knew that there was only one way to achieve that. Mr Cameron has always been a realist who concentrates on actual possibilities, not on might-have-beens. So while much of the rest of his party was saying "if only", David Cameron played the hand that events had dealt him.

For the coalition to succeed, opponents had to be transformed into harmonious colleagues. This meant clear agreements and understandings; ambiguities would breed discord. So a structure of Cabinet committees was quickly established. Thus far, it has created common purpose. So have personal dealings. The coalitionists have discovered that they rather like each other. Paradoxically, this was reinforced by the new government's worst setback, the resignation of David Laws. The Liberals were moved by the sincerity of the Tories' tributes. Shared adversity can bond former adversaries.

The smooth transition to a new government has also involved, and delighted, the civil service. Both sides have been pleasantly surprised. The Tories had feared that they would inherit a demoralised civil service. Civil servants feared that any party coming to power after 13 years would assume that all the officials were its political foes; how else could they have worked for the other side? It is true that most politicians' instinctive grasp of political neutrality is on a par with Don Giovanni's understanding of chastity. But the new lot have advantages. Francis Maude, the Cabinet Office Minister most closely involved with the civil service, had been a minister. So he knows just how good the civil service can be at its best. The same applies to David Cameron and Nick Clegg, who were both special advisers of one kind or another. They, too, understand how much talent is available in Whitehall.

There were fears that much of this had been eradicated by the last government. It never learnt how to use the civil service properly and often appeared to want to turn the entire machinery of government into a giant press office. But the new ministers have been impressed by the civil service's resilience. The officials have been equally reassured by their new masters' business-like approach. Tony Blair preferred to run the country from his sofa. Throughout his premiership, he barely enjoyed diplomatic relations with his Chancellor. Although that changed when Gordon Brown moved to No 10, the era of the big tent was speedily replaced by the era of the flying mobile phone. That is all over. When they put their heads round the PM's door, officials will no longer have to duck.

Nor will they have to indulge ministerial fantasies about micro-managing the entire country. While it is true that not all civil servants are natural deregulators, many of them had come to appreciate the weaknesses of the Brownite approach, simultaneously bossy, meddling and weak. Over the past few weeks, there has been a brisk little bonfire of regulations, mainly Eric Pickles's doing at local government. More will follow. At least outside the banking sector, Vince Cable seems happy to add to the blaze: the civil service, to warm their hands at the flames.

There is another warm glow, of renewed traditions. Michael Gove arrived in his office to replace Ed Balls. Under Mr Balls, the sometime Department for Education was called the Department for Children, Schools and Families. The Permanent Secretary asked Mr Gove what he would like it to be known as. "The Department of Education" was the answer, greeted with a heartfelt "good", followed by "What would you like us to call you?". "Secretary of State" said Mr Gove. The response was another equally warm "good". Formality can often lubricate efficiency, and as those who endured the French Revolution, Stalin's Russia, or Gordon Brown's Downing Street could confirm, informality is no defence against terror.

Partly because of Sir Humphrey, one aspect of Whitehall life is underappreciated. Civil servants approve of strong ministers. Good officials would far rather work for a rude but effective minister than for a courteous and weak one.

There is an obvious reason for this. Able civil servants want to be associated with success, not failure. They do not mind giving up evenings and weekends on their master's business, as long as it will come to fruition: not if he is an amiable lightweight whose proposals will inevitably founder. Give civil servants a Jim Hacker and they will keep him in leading-strings to stop him wrecking the department, but far from relishing that role, they will be praying for him to be replaced at the next reshuffle. So far – though there is plenty of time – the coalition has not yet thrown up a Jim Hacker.

There is one quasi-comic aspect. Downing Street is still trying to accustom itself to Steve Hilton, who is best described as David Cameron's principal adviser on strategy. Mr Hilton does not look like a Tory. He probably thinks that "Pin Stripe" is the name of a brand of beer, or a pop group. Forget ties; in the office, he will not even wear shoes. As he is bald, it looks as if a discalced friar has come to work in No 10. That might not be a wholly misleading comparison, for Mr Hilton is a man of deep moral seriousness. The need to replace the broken society with the big society, the anomic society with the responsible society: welfare reform, education reform – these are Mr Hilton's passions.

As his former colleagues in Conservative Central Office will eloquently testify, Steve Hilton is not a man designed for bureaucratic procedures. It is not that he sets out to subvert them: merely that he never notices their existence. This has led to exasperation, but it rarely lasts long. Shoeless Steve is a man of great charm. He is also a committed Conservative. Both of those more than compensate for his eccentricities.

There can be clashes, especially with Andy Coulson, Mr Cameron's press secretary. Mr Hilton was at Oxford; Mr Coulson graduated summa cum laude from the University of the Essex streets. Steve Hilton has visions of the distant horizons of social generosity. Andy Coulson is focussed on the media, but also on the anxieties and angry feelings of the Tories' lower-middle class supporters. The difference is great; the creative tension could be of equally great value.

So the honeymoon continues. Its current state reminds one of a Wild West film from boyhood. The wagon train is moving contentedly along the Oregon Trail. Everything seems peaceful. But we viewers know that just over the hill, the Injuns are sharpening their tomahawks. In politics, peace never lasts long.