"Love-bomb your sports department," she suggested. (Yowzah!) "Don't employ your mates, like Melvyn Bragg, as it will only cause enormous resentment."
It must have escaped Janet's notice that Melvyn is in there already and has been for many years. He is on what we call the radio.
Janet could benefit from listening to Melvyn's ever-stimulating In Our Time (Radio 4, Thurs, 9am) the programme about ideas and events which have shaped our age. And surely she, of all people, would find The Routes of English (Radio 4, Thurs, 4pm), Melvyn's series on a thousand years of our language, improvingly mega-rad.
Among the former L!ve TV executive's many helpful suggestions to Mr Dyke nestled this small bombshell: "Purge the place," Janet advised, "of its obsession with youth and ratings. You're middle-aged like me..."
Crikey! I'd better have a little sit-down. For it was Janet who invented the phenomenon of yoof TV and, upon her arrival at Television Centre in 1986, did so much to scatter the pestilence across the BBC. Is she, by editing a grown-up newspaper, finally growing up? At this rate she'll be urging us all to listen to Radio 2. And why not?
Janet would not be the only new convert from the rock'n'roll generation to the network and its groovier-by-stealth music policy. On a recent Saturday Music Show (Radio 2, Sat, 3.30pm), Joe Strummer, former ideologue and foaming frontman of punk-rock guerrillas, The Clash, told presenter Billy Bragg - himself a guitar-slinging radical, now shaping up as a first-rate DJ - that "the radio in the kitchen is tuned to Radio 2 and the reason is because it's playing music that's worth listening to. I can't stand to hear stuff that irritates me, vacuous nonsense. I must have music with lives lived."
This was no off-the-cuff, crowd-pleasing remark. A week earlier, in the pub with Joe after we'd deejayed together on my Radio 1 programme, I heard him evangelising for Radio 2 to a chap at an adjoining table. "It's the only music station," he said, as I set about mopping up my pint.
Strummer's radio habits symbolise the unavoidable dilemma in which Radio 2 finds itself, especially since Radio 1 flung itself fully at the 15- to 24-year-old audience: Joe does not tune to Radio 2 for Jimmy Young (Monday-Friday, 12 noon). Nor is he hungry, at 47, for Sing Something Simple (Sundays, 4.30pm). Equally, the Cliff Adams Singers, who have yet to sneak "White Man in the Hammersmith Palais" into their repertoire, are not quite ready for Joe.
But like many largely disenfranchised listeners over 24, who don't want to listen to commercial radio or speech-based local BBC stations, Joe feels at home with Radio 2's excellent specialist music programmes and the network's expanding sense of Radio 11/2.
The gulf between Radios 1 and 2 is also problematic for Joe as a recording artist. Where - apart from on Billy's Radio 2 show and on my own Radio 1 programme - will his new album, or the recently released live Clash CD, be played? Well, nowhere.
The Clash were the last word in rock'n'roll bands and the new CD, recorded when they were at the peak of their powers, confirms that nothing in the past 20 years has come close to matching their energy and elan. But Steve Lamacq (Radio 1, Monday-Thursday, 8pm) cannot play it because, apparently, 15- to 24-year-olds haven't heard of The Clash. (Hmm... and given the chance they might also realise just how dreary so much contemporary indie rock and dance music really is...)
Meanwhile, Ken Bruce (Radio 2, Mon-Fri, 9.30am) is disinclined to wallop us with "Clash City Rockers" off the back of a Drifters oldie - for the time being anyway. But there came this week a thrilling indication that controller Jim Moir's evolution-not-revolution policy of redefining Radio 2 may be picking up speed: Sir Cliff Richard's new single, "The Millennium Prayer", will not be put on the playlist. The track, which sets the words of The Lord's Prayer to the tune of "Auld Lang Syne", ferchrissakes, has been excluded not because Sir Cliff is getting on a bit, as has been reported elsewhere, but because it is a load of sanctimonious old shite. Mr Moir, I am ready to defect.
Joe Strummer will present a series of music programmes, `Joe Strummer's London Calling', on the World Service from 9 Jan