Where would their backup have been before? I know the other Global brands’ backups would have been at one of the regional studios, but LBC is obviously national from London.
Based on, and continuing how radio stations got through lock-down, I'd be considering a virtualised de-centralised solution for disaster recovery, rather than decamping everybody to an alternative building?
It's still fully equipped to run the radio networks as it was from the GWR/early GCap days when it was the network hub. It has a lot of studios and office space, formally full of life, now sitting empty solely for this purpose.
As well as serving as a backup network hub via the local sites, it also has the capability to dial in to the transmitters and take over their output if needed, which would be required for the London stations if Leicester Square is evacuated.
In the Chrysalis days I seem to remember that LBC's DR studio was at TalkSport and vice versa. Certainly one morning both breakfast shows were coming from adjacent studios due to lack of power in one