I wouldn't worry about your other choices being Maths as opposed to Statistics. I'm a fresher who's doing BMS this year, and the rest of my applications were pretty much Economics!
Also bare in mind that they can't see what other universities or courses you are applying to, so it doesn't really matter as long as your Personal Statement is somewhat relevant to the course.
As for your grades, you did better than me in your GCSEs, and I did exactly the same A levels (and got 4 As, as you are predicted).
If you want a read of my Personal Statement then feel free to PM me and I'll dish it out.
On the subject of your parents making you apply to LSE, if you were to get an offer from it, would you be likely to accept it? If not, then there's not much point in applying and worrying about not looking more statistical, when you could just as easily apply to a university you would rather go to. After all, if there's pressure from your parents on you to apply to LSE, imagine how much pressure there will be to accept the offer if you got one!