Challenge hooligan view of Englishness
Somebody in politics has to remind us that governing is not just about efficiency, but also about beliefs and values. The Home Office - whose complex and diverse responsibilities defeat most incumbents - is especially good at turning ministers into servants of the management machine, tackling crisis after crisis, drowning in numbers and beset with legal detail.
That is why a politician who reminds both himself and us that there are causes grander than the crime statistics, is to be cherished.
Recently, quizzed by Sir Herman Ouseley about how to tackle the chronic problem of young men's violence, particularly around football matches, Straw outlined his familiar policies for policing and the use of legal restrictions against the hooligans.
But he then went where most ministers would not. He pointed out that much of what passes for support for our national teams is a feeble-minded, confused effort to bring life to some dimly-remembered patriotic cliches.
In the minds (I know I'm taking a liberty with the use of the term "mind") of those who shame us abroad and at home, there is a vague catalogue of English pride which includes Richard the Lionheart, Laurence Olivier at Agincourt, the Battle of Britain and the 1966 World Cup victory, all wrapped in the flag of St George.
This ludicrous pastiche serves as the framework for assault, battery and damage to property, asserted in the name of England. It would be laughable if it were not so serious.
Few current ministers would have the courage to tackle a sensitive issue like football hooliganism with reference to seemingly abstract concepts such as identity. Perhaps only the Chancellor, who actually reads books - as opposed to briefing documents - would argue at this level.
Gordon Brown too worries away at the issue of identity; many of his speeches focus on the question of what it means to be British, and ask how a modern, multicultural society can survive in an era of rampant devolution.
Unwittingly, both men are presenting serious challenge to their colleague, David Blunkett.
There are two areas in which schools and universities are going to have to answer the Straw challenge.
One is in the national curriculum. The new version of English history has expanded the traditional syllabus to incorporate new perspectives, including those of the poor and of peoples colonised by the English. So far so good. But in our determination to move away from a jingoistic, narrow view of English history, have we lost sight of the need to invest our nation with a sense of identity?
My own view is that an entirely new view of the making of the English could be promulgated, and I was surprised and delighted to see it shared by Jack Straw.
He pointed out that the indigenous English were really the people who now occupy Scotland and Wales. They had retreated under the successive waves of immigrants who now populate England - from the Danes, through the Normans, Italians, Jews, up to the Irish, East African Asians and Caribbeans.
In essence, the story of the English is quite the opposite of the hooligans' view of 1,000 years of unbroken Anglo-Saxon hegemony. It is, in fact, the tale of the most successful pro-refugee and asylum policy anywhere in the world, since the fall of the Roman Empire.
The other dilemma Straw and Brown raise for Mr Blunkett is the future of religious and culturally-specific schools. If we want to reassert the nature of Englishness in English schools, even if it is in the diverse form I've outlined above, it may not be to the taste of some - Jews and Muslims, for example.
Should such groups have a stronger claim to independent, separate insitutions, which, whilst fulfilling the national curriculum and other standards, place greater emphasis on their separate traditions? It's a complex and difficult issue, involving the reconciliation of some fundamentally opposed sets of values. But after all, that's politics.
Government should be about defining what we believe, or else we'd leave it all to the management consultants. And they've already got enough out of us, thank you very much.
Trevor Phillips is chairman of the Greater London Authority