Firstly there are perhaps a dozen LC frequencies. The other thing is that LC won't talk to you unless they can see your tail # on their computer, and for that to happen there has to be some prior coordination.
True, although calling the one that you last spoke to on your way to France might work...I only suggested it because leaving Scotland the other day I wanted to get my IFR clearance, not knowing any different I called Scottish Information while still on the ground, only to be told to call Scottish Control, it took them about 2 minutes to find my plan. London perhaps work differently but Scottish didn't seem to have a problem with picking me up 'from scratch' as it were, coming from a airfield with no radio in the open FIR. Perhaps the ATC forum could help on this one?