Death is usually good for sales. The assistants in the largest London branch of Waterstone’s report that, on Wednesday afternoon, almost all the fairly small stock of books by Clive James disappeared from the shelves. It was as if a certain generation of readers had suddenly remembered how entertaining he was. The coincidence of his death being reported on the same day as that of Jonathan Miller (though in fact they died three days apart) struck many as significant. As a letter to this newspaper put it, “In a world increasingly populated by charlatans and idiots, we have just lost two outstanding, intelligent, funny and talented individuals in one day”.

Were they the last representatives of a special kind of public intellectual? The polymath as entertainer? There are still plenty of public intellectuals, but they are not often funny and not so often on TV any more. What James and Miller shared was a habit of cultural irreverence that was only possible because of their love of culture. Both flourished in part because British TV at the time had more confidence in the wits of its viewers. Almost every obituary notices James’ delight in moving back and forth between high and low culture. British TV, it should be said, gave him many opportunities to do so in the early 1970s, when he began writing his Observer columns.

And what did the television schedule at the time, as reported by James, look like? An hour-long interview with Harold Pinter rubs elbows with a report on the lyrics of leading contenders in the Eurovision song contest. A Ken Russell film about Wordsworth and Coleridge is found more absurd and less entertaining than an episode of the current affairs programme Nationwide featuring child impersonators. Of course, it took James to find out the incongruities. Analysis of the latest episode of Dallas (of whose delicious absurdities he was a connoisseur) would be illustrated by an epigraph from Nietzsche. James’s prose had a kind of deadpan poetry in which you heard his voice. I still recall his description of a piece of footage that I had actually seen a few days earlier: ski jumping from Kitzbühel, where a competitor lost one ski in mid-air. James imagined the jumper (otherwise immaculate) having to decide whether to land on the foot with the ski or the foot without. “He chose the leg without – a huge error.”

Both men were proof against charlatanism by openly suspecting themselves of such. Miller was comically self-conscious about his own contradictions. (Thus, the perfect title of Kate Bassett’s excellent biography of him: In Two Minds.) Not the least of these was his attitude to the medium that made him familiar to millions: television. He sometimes seemed to think that TV numbed the mind, yet he ended up becoming a vivid TV personality. In his own recent memoir, his son William recalls how his father refused to have a television in the house, until he fronted his own multi-part series The Body in Question. Watching Miller, in that series, convey lessons about medicine and health even as he sickeningly experienced increased gravity in a looping plane, or put on a face mask that gradually reduced his oxygen intake, you wondered whether the comic aspects were intentional or not.

TV made them famous for their voices and their faces and their bodies: James, a genial retired prop forward; Miller, a performance artist of long, tangled limbs. It is extraordinary to think that James once fronted a primetime ITV show that traded on his sardonic wit. Miller, in contrast, was a BBC man: in the index to Bassett’s biography, the single longest entry is “BBC”, while ITV has no entry at all. Miller was confident that TV could give us Shakespeare or a multi-part inquiry into the nature of language or an engaging history of atheism. James, the natural TV aficionado, ended up seeming more doubtful. His 1995 address to the Royal Television Society was entitled Bring Back the Overqualified. You get the drift. He once thought that TV could be entertaining while “delivering enlightenment to the public”, but by then had started thinking that it did not want to do this any more.

None of the undergraduates whom I asked last week had heard of either man – but that is hardly surprising. Clive James and Jonathan Miller may have shared an educated reverence for the art, music and literature that could outlive its times, but both men lived for the fizz of their own cultural moment. Miller’s productions of plays and operas live on in the memories of those who saw them (and, evidently, in the memories of those who performed in them). You can read James’s collections of TV reviews today, but if you read them first in the newspaper then they have done their work. If the two men belonged to a lost age of “the overqualified”, it was because both knew enough to think that they were hardly qualified at all.

• John Mullan is professor of English at University College London