Last Night's Television - Holby City, BBC1; The Many Faces of June Whitfield, BBC2

People giggled when I said I was going to be reviewing The Many Faces of June Whitfield. What was it? The mismatch between the fusty bombast of the first half of the title and the slightly parochial connotations of the subject? Would the name June Whitfield have done it on its own – as a marker of a very Middle English type of comedy – or did it need the mildewed showbiz-bio description as well? It is, you'd have to admit, the kind of title that keys you up for a spoof. It's got something of "Balham – Gateway to the South" about it, an association that wasn't exactly dispelled by the opening line of the voiceover: "For more than 60 years, one woman has been at the beating heart of British comedy". But while Steve Coogan – the Inside Story took the very wise precaution of sending itself up now and then, The Many Faces of June Whitfield was played absolutely in earnest. Tongue and cheek never met once as a parade of approbatory clichés ("consummate professional", "pin-sharp timing", "joy to write for") filed past. If this documentary had been a person it would have been wearing a Pringle sweater and a silk cravat, just as Nicholas Parsons was, in fact, when he popped up to hymn June's indispensability to the string of top-of-the-bill comics she'd worked with.

It wasn't that the praise wasn't deserved, particularly, or that the clips didn't back up the remarks about comic timing and all-round trouperliness. It's just that the phrase "always in work" – however proud a boast for any actor – isn't a lot to build a panegyric on. And the longer the thing went on the more it became clear that Whitfield had sustained her career partly by never letting her male co-stars down but also by never threatening to overshadow them. "June's always known that you're in a safer place if you're not top of the bill," said the comedy producer Jon Plowman and even the voiceover summed up her Sixties career as "carving out a successful niche for herself". She didn't demur either: "Maybe the reason I've worked with so many of them is that I'm no trouble," she said at one point, a decorously modest remark that struck you as having a lot of truth to it too. And though it's no small matter to wrangle egos as unwieldy as some of those she worked alongside it still seems an underwhelming claim to fame.

More telling perhaps – about her durability in the business – was an appearance by Miriam Karlin, who started at Rada on the same day as Whitfield during the early years of the Second World War. She remembered a brief foray onto the Broadway stage in 1952: "I would come in pretty stoned, having done a lot of... naughtiness," she explained, and she would find June sitting up in bed calculating who owed what to whom down to the last cent. June was the sensible one, in other words, the one who could be relied to turn up on time, hit the mark, and never forget the lines. Miriam Karlin now looks as if she could be June Whitfield's mother, but you couldn't help but feel that an account of her life might have been a little racier in its detailing. It wouldn't have had to cope with the Terry and June problem either, which I suppose you can reasonably describe as "one of the most enduring sitcoms on British television" but only in the sense that it felt as if it went on forever. The truth that nobody quite dared say aloud here is that one of the reasons Whitfield's career flourished in recent years was precisely because Terry and June had become so axiomatically dreadful. She was initially hired by the alternative-comedy generation as an ironic gesture, a kind of mascot of the comedy that they'd displaced. It's a credit to her talent (and her character) that she was good enough to outlast that essentially limited gag – but "national treasure" still seems to be pushing it a bit.

Business as usual in Holby City, which is where British character actresses are sent if they've been really naughty. I'd love to have an NHS efficiency consultant do a time and motion study on Holby because it's frankly astonishing that any of the patients leave alive, the staff being so busy looking stricken or lovelorn at each other. There was a brief flurry of medical interventions at the end of this episode, but it didn't interfere with the bedside relationship counselling or the time-sucking quantities of intercollegiate rivalry and mutual suspicion. What's so funny about Holby City is the way that notionally delicate conversations and whispered confidences are conducted in the least discreet spot available, in one instance here over the open chest cavity of a dying woman. Anyone in search of a comedy masterclass should watch, but, you know, I don't think this is meant to be a spoof either.