Well, I have no clue but I can try to guess by what you said. If LSE really gives out 3 offers per place, then I would suppose KCL gives out about 5-6 offers per place. LSE is one of the hardest unis to get into and they also have higher requirements than KCL.
So let's say there are 12 applicants / place at KCL (that's just a guess, but you can find the numbers on their site) then you should have a fair chance of getting an offer atleast- something like 50% =]
Maybe I'm just a freak, but this seems logical to me =]