It may have been the case that Parliament was sitting, and any decision for the UK armed forces to be part of a war collition would almost have to be debated beforehand, probably taking over that afternoons scheduled business, so that may have been the thinking of the switch of locations.
I'm sure that was the case, there have been other examples in recent years of Question Time moving location at the last minute because of breaking news, and as you suggest, the fact the war began that day and presumably senior figures would all have been in Parliament means moving it to London would have been an obvious response. The Barbican was the regular location for Question Time when it was in London in those days (which is was far more often, it would only go somewhere else about once a month) which was something of a step up from the Greenwood Theatre.
Peter Sissons talked about this 1990-91 series of Question Time in his book, it was the only series they ever broadcast live and it coincided with a huge period for news, especially on Thursdays. On the night Thatcher resigned, apparently there was supposed to be a Panorama special that night but it was never finished in time (Sissons says at the height of Birtism, when everything had to be double and triple-checked, the production team simply couldn't cope with the deadlines) and so Question Time volunteered to fill the gap and they did two episodes that night, and similarly they were able to extend it on the night the War began as well.
Sissons says everyone was very pleased with how exciting it was now it was live, and he was really excited with the ways things were going as they had a new editor that year who was brilliant. But then in quick succession one episode had to abruptly end after ten minutes because of a bomb scare, and then one failed to make it on air at all because of a power cut, which put paid to the live broadcasts, and then at the end of the series the Beeb announced they were contracting it out to an indie, and despite Sissons lobbying hard to keep the editor, they wanted to bring in their own, and Sissons never thought it was as good again.