I think the crux of the matter here is that London Info, on a busy day, is woefully inadequate for the type of service the GA community is expecting of it. Things have to go one of two ways.
1) The country is split into 3/4 regions, 1 of which should encompass the south coast as far as the Solent and the respective part of the channel to provide the FIS and alerting service that it is there for. No reason why these shouldn't be bandboxed during quiet periods or seasons, but in the height of summer split.
2) Disband it in it's present guise and have two frequencies. One would be a purely INFORMATION frequency to enable to get weather and possibly airways joining clearances - NOT traffic information. The second would be a self announce unicom so that VFR traffic can pass position reports and separate itself (which is the whole idea behind VFR I was taught). If you need to scream Mayday then 121.5 - it doesn't take that long to dial it up and if you're over the channel you'd be high enough to have sufficient time to do it.
I've crossed the Channel and dialled up London Info on a Bank Holiday Monday. It was probably the most pointless exercise I've ever committed due to the amount of people using it over the area it covers, and this is compounded by the fact that people pass the standard contact message with estimates in the hope that they will get adequate traffic information - on the whole it isn't going to happen as it's physically impossible.
Time for a rethink I would say
CM