I think that most of the medicine applicants are interviewed. If you don't really love your subject (and therefore, medicine), you run the risk of making it evident at interviews. Moreover, since medicine is one of the most competitive courses, if tutors notice that you don't really like it, you're very likely not to be offered a place. Last but not least, since LSE requires a good personal statement for finance (and since you will have a medicine one), in the very unlucky case of being rejected by those four Unis, you'd find yourself in big troubles.
Moral of the story: fight and chase *YOUR* dreams.
I know that this is very hard to do, but if you talk to your parents and explain them that you don't really like medicine, I'm sure they'll understand.