Didn't the Big Breakfast do some kind of marathon broadcast on Channel 4? I vaguely remember seeing something in the small hours and thinking it was better then the pompous stuff BBC1 were putting out.
Yes, it ran 12.30-9am, and even then managed to overrun by half an hour. Actually at midnight was Graham Norton, most memorable for Raquel Welch appearing via satellite and at the end announcing "I hope you reach a higher level of taste in 2000" before the link failed, and Graham said, "Well, happy new year to her, the grumpy old bitch". But apparently it was because she couldn't see what was going on, only hear it, and it sounded more disgusting than it was, and Graham apologised to her later.
ITV did Countdown 2000 throughout the day, where the newsreaders would come on at the top of every hour - including in the ad breaks in films and dramas - to introduce the latest midnight, and then they did an hour-long show at 11pm. They were in the normal ITV News studio and I remember the lunchtime news - which was Julia Somerville's last bulletin - was presented from armchairs, which was the only time they did that.
And BBC2 simulcast with BBC1 from 11.50 to 12.05, before that they were doing their own thing. Jools Holland was on the night before, December 30th, and the Scottish opt-out was on BBC2.