Where they live though? Or pre recorded?
Well, they were certainly sold as being live. It's funny how they seemed to be just as big stars as on the Beeb now, but they did absolutely bugger all in the ratings. They weren't related to the current BBC1 concerts, they just happened to be a concert on New Year's Eve - in much the same way BBC2 used to do one in the eighties.
There was a live episode of Des O'Connor Tonight in 1987/88 with live links across the UK, that would presumably have been a suitable alternative to the Beeb showing 'stEnders up to midnight. After that it was a load of odds and sods before in 1991 we got what we had for most of the nineties and what we get now, just the news at midnight, sometimes in the middle of a film.
The John Leslie one mentioned up there was probably the one in 1997/98 when they were live at Edinburgh Hogmanany, but I think that was just the STV coverage networked (as was the case up until the mid-eighties) rather than anything special for the network as a whole.