The Week In Radio: When Joan opened for The Rolling Stones

God bless Joan Rivers. Last month, the 75-year-old gargoyle with the rapier tongue suffered the indignity of being booted off ITV's anodyne chat show, Loose Women, for letting loose a volley of expletives. Did the producers not realise that this is Rivers' shtick – and has been for the last 40 years? In any case, the incident made her a particularly delicious choice to present Ed Sullivan and the Gateway to America (BBC Radio 2, Tuesday), a documentary about the censorious TV host who ruled the Sunday-night ratings for 23 years.

Surprisingly, Rivers had been a guest on The Ed Sullivan Show herself, in the same 1967 episode in which a sulky Mick Jagger was forced to sing "Let's spend some time together" instead of "Let's spend the night together". Sullivan apparently greeted the artfully mussed Stones with a curt, "You'd better clean yourselves up, boys", and marched them off to wash their hair, before turning his attention to their smutty lyrics.

There could have been more from the comedian about her experience, but this was a fascinating chronicle voiced by Rivers in a smoky, Botoxed slur that, like the show, sounded like it had seen plenty of action.

Sullivan makes an unlikely pioneer of modern television. Plucked from pounding the Broadway beat as a hack in 1948, he found himself presenting a weekly variety show (six acts, $400 budget) that, in an effort to appeal to all demographics, would schedule The Beatles alongside a virtuosic display from a canine football team. Old Stone Face exercised strict control over his acts, vetting the routines of comedians in his hotel room before the show (though he had, apparently, no sense of humour), and gauging the political sympathies of his guests in order to weed out any Communists.

He also refused to host Elvis Presley, declaring him unfit for the family living room, and only backing down after he realised The King's ratings potential. Paid $50,000 for three appearances, Presley's debut broke records, with 16 million viewers – and almost as many complaints. To sugar the pill for the second, Sullivan introduced Presley as "a decent, fine boy who is quietly working hard for a Hungarian-relief charity", and saddled him with a children's choir from Ireland. Pleasingly, the programme tracked down one of the choristers, who read from her diary: "Had rehearsal with ES. Show at 8 o'clock. Mounted police holding back howling mob." By the third show, Elvis was filmed from the waist up only.

Earlier in the week, it was the turn of another comedian. Lenny Henry's What's So Great About...? (BBC Radio 4, Saturday) seeks to debunk various cultural concepts, from Bob Dylan to life coaches. This week's theme was method acting, which made for a mildly diverting half-hour, though, like Rivers, Henry added little except a distinctive voice (key on radio, granted). He traced the frequently ridiculed acting system used by such greats as Marlon Brando, James Dean and Dustin Hoffman to its source, the Actors Studio in New York, where a teacher initiated him in its impenetrable ways. "Your job in Act I, scene 2, when the phone rings, is to behave as though you didn't know it was going to ring", he explained, recalling Ian McKellen's hilarious coaching of Ricky Gervais's jobbing actor in Extras: "How do I act so well? What I do is pretend to be the person I'm portraying in the film or play..."

But Henry was sold, concluding that "the Method rocks". I'm still with Laurence Olivier who, confronted by a sleep-deprived, method-acting Hoffman on the set of Marathon Man, famously blustered, "Why don't you just act, dear boy?"