Stay Tooned was essentially a replacement for Rolfs Cartoon Time after he went off to ITV.
I remember Disney Time being one of the staples of bank holiday BBC, along with World's Strongest Man
Yes, a good trivia question, this - David Jacobs did the first, Rio Ferdinand the last, what was it? It's Disney Time. As you say, it was a Bank Holiday staple, in the eighties there were four episodes a year, at Christmas, Easter and the late May and August Bank Holiday. In the nineties I always found it a bit strange that it was on the Beeb when all other Disney was always on ITV, but it carried on up until 1998. In fact on Christmas Day 1998 they was a Disney Time-branded programme on ITV, but I think that was the only time they used that branding.
Rolf Harris Cartoon Time began in the late seventies, and I remember reading in his autobiography (which I've long since thrown out) that it only came about as the Beeb had bought a package of several hundred cartoons and wanted to do something with them. As you say, Stay Tooned replaced it when Rolf went to ITV in 1989, from the same production team, but it was a bit more involved and had more discussion, and showed animation from all over the world rather than Cartoon Time's non-stop MGM and Warner Bros. I remember from the Radio Times it was produced by Nick Freand Jones who at the same time was also producing Moviedrome (and I noticed produced Mark Kermode's recent series).
I remember this, on Christmas Eve 1990, it went on for over an hour, clearly Cartoon Club had done well enough to allow them an additional budget for a foreign jaunt.
I know it's not a very good name to drop now but I used to love Rolf's Cartoon Club, I found it fascinating. I was in the club as well and I remember in the newsletter once there was a feature inspired by a letter from someone who had bought a VHS called Bugs Bunny And Friends (which I also remember renting from the video shop) only to find it contained one ancient Bugs Bunny cartoon and then a load of black and white obscurities from the thirties, and they discussed how at that point, Warner Bros only had the rights to their post-1950 cartoons and all the older ones were up for grabs to anyone who wanted them, hence this video. And at that point I remember ITV had what we considered the "proper" post-1950 Warner Bros cartoons and the Beeb had the older ones. Of course nowadays thanks to various bits of consolidation they own them all again.
It was always a bit of Russian Roulette when you saw "cartoon" billed in the TV guide as you never knew what you were going to get. On the Beeb you would always hope for Tom and Jerry or Droopy but you'd sometimes get one of those ancient pre-war Warner Bros ones (I remember them showing one of those in CBBC once, and Andi Peters unable to disguise his amusement at how old and boring it was), and on ITV you'd always hope for Bugs Bunny or Daffy Duck and it was such a shame when you got a rubbish Disney one instead. Was there ever a more disappointing image for an 80s kid than Mickey Mouse's giant head at the start of a Disney cartoon?