If you'd suggested to me then that this slightly geeky lawyer, a committed supporter of the campaign to boycott Chilean goods, might one day be in the delicious position of having to decide what to do with General Pinochet, I would have told you to lay off the dope. But there he is, a former student activist who now has the power to bring a little moral justice to bear on this grotesque, swaggering, old monster.
But things change. I can recall that in my first term at university I watched as he and one of his far-left critics in student politics rowed their way through a week-long conference, at the end of which she presented him with a "retirement" present - a mock bomb, round and black with a wick at the top.
That same far-left scourge, Kate Hoey, by the way, is now MP for Vauxhall, a committed Blairite and one of Jack's ministerial team at the Home Office.
Straw is the grand patron of a new, exclusive and increasingly significant club in British public life, of which I myself am a modest member. Barely a week goes by when I don't run into someone holding a responsible position, who reminds me that we first met at some National Union of Students Conference more than two decades ago.
Some attention has been drawn to the fact that there are no fewer than six former NUS presidents on the Labour benches. But no one has yet done an analysis of the depth of the penetration of the student movement into the New Establishment. Some may have been formally connected with the NUS, such as Schools Minister Charles Clarke, a former president; some more loosely, such as Chancellor Gordon Brown, whose first election victory was to become the Rector of Edinburgh University.
As he gleefully recounts, just out of his teens he found himself chairing the university court, and banging the gavel on the distinguished academics and businessmen who had previously run the university's affairs.
But it's not just the headliners who matter here. There are hundreds of people who entered adult life via a stint as student union activists.
In the past week, I have run into half a dozen members of the club. They include a Cabinet Minister's Parliamentary Private Secretary, a leading broadsheet writer, a senior executive of the company that runs the lottery,the head of corporate affairs for one of our most famous retailers, the boss of one of the private sector's most effective lobbying organisations and the head ofa major educational trades union.
In itself, it's a phenomenon, and no doubt someone will write a book about it. However, this isn't just an ironic reflection on the way that we all grow up and lose our hair and youthful passions in roughly equal amounts.
To understand the full significance of what's happened here, it's worth remembering why there are so many such people, and the particular atmosphere in which they went into higher education.
As I watched the MPs flooding into the House of Lords to hear the Queen's Speech last week, I thought if I were producing the TV coverage I might have superimposed a ghostly figure over the ermine tide. The late Lionel Robbins is now probably best remembered as the author of a standard text on economic history; but as Lord Robbins, he was chairman of the Committee on Higher Education from 1961 to 1964.
It was his aggressively democratic and expansionist 1963 report that created a vast new group of undergraduates of a kind never before seen in British universities. Bright men and women from working-class backgrounds had always gone to college but, for the first time, Robbins, who argued that higher education should expand according to demand, made it possible for such people to enter university in vast numbers.
Indeed, within a few years of Robbins's own report, it became clear that the actual demand would outstrip his estimates by at least a third. The result was, I think, a student population which revelled in its new-found diversity, even classlessness.
Amazingly, these people are now running the country. The Robbins generation is different to all that has come before. Its substance may still be a little opaque, but its style is clear - politically open, modern and reformist, but in the execution of its policies ruthlessly focused and determined to get its way.
On occasion, they are too cautious, and they can surprise and disappoint; the Home Secretary last week made a series of deeply restrictive, and somewhat unimaginative, proposals for dealing with refugees. His officials might do well to go back and read some of the speeches and articles of Jack Straw, defender of the rights of dissidents and overseas students. But taken overall, the Robbins generation is a breath of fresh air. And I don't yet think we've seen the best of it yet.
Trevor Phillips is a broadcaster and journalist