I think the only time a European qualifying session wasn’t live was the French Grand Prix in 1999. I seem to remember it was a rights dispute when Bernie Ecclestone claimed the contract they signed hadn’t included qualifying. The Wikipedia article refers to it being an ITV ‘choice’ not to, could be both are right! Whatever it was, it was just the one race that was affected.
It was actually a couple of races that were affected, as you mention it was a contractual dispute as there was some kind of confusion as to what they were actually allowed to show live. So for a few races they showed the qualifying as live at about 3pm. The British Grand Prix wasn't affected because they were the host broadcaster but I think the races either side were affected.
Then the following race had the qualifying billed as being as live at 3pm again but they managed to resolve the dispute a few days before and it was shown live. Unfortunately that day's SMTV had been pre-recorded, so Ant and Dec had to come in just to film an extra link at 11.30 (I remember they had to do it outside the studio, presumably the set wasn't up) to say that despite the fact they'd been saying all morning that CDUK was going to be at 11.30, it was actually now going to be at 1.30 after the F1.
The US GP started at 7pm, with the ITV replay being at 10.45pm. The justification was that while they were happy to interrupt the Summer schedule during June, the late September date was a little more awkward. Canada during ITVs days was a 6pm UK start, and the TV schedule would normally have Corrie being at 7.50pm, but for some reason, every year we'd get messages on screen from 7.30, during the final laps reminding us that a program which was not even due to start for another twenty minutes, would follow the F1!!!
Most of the time, the race would overrun anyway, and it would normally be about 8pm it would be off air by.
Yes, the Canadian Grand Prix was a familiar fixture on Sunday night ITV, for the first few years of the contract that was the only one that was in primetime. It also meant BBC1 would have to shuffle around their schedule to avoid the delayed Corrie going up against one of their big dramas. As mentioned, they were prepared to do that with the Canadian Grand Prix in June but when it came to the US Grand Prix, they weren't willing to give up the vast majority of the sacred Sunday night for that.
The bizarre thing about the US Grand Prix in 2000 was that, after the as-live showing on ITV at 10.45, the highlights show was at 3am, which hardly seems worth doing. The following year it was live on ITV, and that year of course it was a major news story as well, just a few days after 9/11.
The other thing about the Grand Prix was that I remember a couple of times that because of the Malaysian Grand Prix at 7am and the displaced GMTV, and the fact the repeat of The Premiership had to be off air before 10.30am, they ended up showing the Premiership repeat at 4am.