IMHO, this is a very good reason for always getting an FIS. We're all human; one can miss things on NOTAMS. Talking to London Information is the belt and braces approach to cross country flying.
Maybe, so long as people don't come to rely on London Info or any other FIS as a substitute for checking NOTAMs. We have had people blunder into the display area around Old Warden (not a TRA but notified active - and an ATZ) and on asking if they have checked the NOTAMS have admitted they haven't. I wouldn't necessarily expect London Info to be aware of every display taking place on a particular day.
Conversely, we do get more people calling for traffic info and transit, so these people are reading NOTAMs