With the Blair-Brown transition finally accomplished – and in exactly the smooth and orderly manner of which Gordon Brown always dreamt – the new Prime Minister must quickly achieve three political objectives if he wants to maximise his chances of securing a personal political mandate and to minimise the risk of his dream turning into the nightmare of general election defeat.

Mr Brown, in his brief statement yesterday from the steps of Downing Street, showed a perfect understanding of what these objectives are. First and foremost, he must prove that the Blair-Brown transition represents a genuine change of government. In his three-minute speech, the word “change” was repeated eight times. Secondly, he must restore some trust in government after Tony Blair’s decade of spin and prevarication. Thirdly, he must prove to voters, and especially to traditional Labour voters, that he lives in the real world of ordinary people, rather than floating ethereally, like Tony Blair, in a parallel universe of foreign presidents, global celebrities and business tycoons. Significantly, the only important polling question in which Mr Brown consistently lags behind David Cameron is the one about “understanding the concerns of ordinary people”.

Mr Brown understands these challenges, but to judge by the snippets emerging about his intentions in government, he has no idea how to meet them. If the new Government’s first few weeks are dominated by announcements of constitutional reforms, ministerial reshuffles and restructurings in the Civil Service or the NHS, Mr Brown will not just be failing to send a message of change. He will be signalling that, just like his predecessor, he lives in a self-deluding mental world of semantic abstractions, far removed from the realities of everyday life.

What, then, could Mr Brown do to convince the country that it now has a down-to-earth government of honesty and change? The answer is “plenty”.

The most obvious opportunities are in foreign policy. Iraq was not just Mr Blair’s most unpopular policy, but also the symbol of his dishonesty. Unless Mr Brown distances himself from the Blair-Bush policy on Iraq, his generalised promises of change will not just be futile but worse than that: they will reinforce his own reputation for dishonesty.

Luckily for Mr Brown, a decisive policy shift on Iraq would now be quite easy to accomplish. Since Britain’s troop numbers have already been reduced to just 5,500, the new Prime Minister has merely to promise to continue and complete the withdrawal within a timetable agreed with the Iraqis, removing Mr Blair’s transparently dishonest proviso that British troops will only be withdrawn once “security conditions allow”. Everyone knows that the real determinant of British troop numbers is not the security situation in Basra, but the political situation in Washington, where President Bush desperately needs to show that his bungling in Iraq still has the support of one remaining international ally. This is exactly the impression Mr Brown must now reverse. Until he does so, everything else he tries to do in foreign policy will turn to dust.

But while foreign policy shifts could go a long way to confirm Mr Brown’s commitments to honesty and change, they would do nothing to advance his third objective. Far from showing that he is in touch with ordinary voters’ concerns, preoccupation with foreign policy would send the opposite message, as it did in Mr Blair’s final years.

Clearly Mr Brown must refocus his Government on domestic issues, especially health, education, crime and taxes; but in the priorities he sets among these policies he seems to be on the brink of making some serious misjudgments. The subject on which Mr Brown feels personally most passionate is education, as he made clear again yesterday in the most heartfelt passage of his Downing Street statement: “I grew up in the town that I now represent in Parliament. I went to the local school. I wouldn’t be standing here without the opportunities that I received there.”

Yet politically he seems to believe that his top priority, both for new legislation and for government spending, must be further reform of the NHS. This seems to me a big mistake: education and crime are now much bigger problems than health for the British public. They are also much more fundamental to the real responsibilities of an effective government.

Law and order and decent universal education are genuine public goods, which can only be guaranteed by governments. This is not true of health, which can be and is provided by a wide variety of private and public arrangements around the world. Moreover, the NHS has already absorbed enough public money and suffered enough administrative upheavals. It now needs a long period of stability to establish whether it can provide reasonable value for its new enhanced budgets, or whether it will ultimately have to be replaced by partly privatised social insurance, along Scandinavian lines.

In education, by contrast, the need for change is more apparent than ever, especially at the secondary level – and at the bottom of the achievement spectrum, not the top.

If Mr Brown really wants to show that he can think afresh and that he is in touch with the concerns of ordinary voters he should recognise that the people of Britain are far more worried about the daily disappointments of their children’s education – not to mention the physical threats they face on the way to school, as they run the gauntlet of outlaw gangs increasingly addicted to violence – than they are about occasional inconveniences in their far less frequent contacts with hospitals and doctors. Britain’s public policy debate now desperately needs to be reorientated from elite issues, such as recruitment to universities and grammar schools, towards the real social challenge of the past two decades, which has been the emergence of a small but dangerously uneducated and increasingly alienated, violent underclass.

There are many other policy areas – for example, housing, nuclear power, prison reform, asylum and Europe – where Mr Brown could quickly take the initiative and show that he is more decisive, more honest and more in touch with Britain’s real problems than his predecessor. But it will be above all in dealing with the underclass that Mr Brown will have to show whether he can embrace new ideas and connect with the real concerns of the British public.

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