Actually London FIR is split into three frequencies, which most of the time are deadly quiet and all worked by the same FISO. About a dozen (sunny bank holiday/weekend) days a year things go ballistic and everybody suddenly wants to go to Le Touquet. Then the frequencies are split and on FISO will work SE England, the other will have SW and N England. You still wont be able to get a word in edgeways though, so had better consider whether you feel safe flying on such a day. I you do, then good, BUT keep a VERY good lookout as you aint gonna get much of a service from anyybody. If you would prefer to fly a weekday, then you can take advantage of the (mostly military) LARS, FIS, passing aerodromes etc and they will mostly have all the time in the world for you and tell you about traffic miles away that you couldn't hit if you tried.
I always like to let someone know who I am so that if I call Mayday and my callsign someone will alrady know who I am, roughly where I am and start looking for me.