A friend of mine from the MBA went through the same situation. He had an offer at BCG in one country, then he wanted to relocate (out of personal reasons) to another country and he had to go throught the whole interview peocess in the new office again. He evetually got an offer at the new location, but the whole thing lasted so long, that he had already accepted another job elsewhere in the meantime.
Changing office after you have already started working there, instead, would be very different. The "ideal" way to change office would be that:
1) You start working where you have an offer
2) You try to network with your new target office (in this case India)
3) Maybe you manage to get located to a project there. In the best case, you start working there "in practice" (one projects is always followed by another one!) although you still "officially" belong to the London office
4) After ensuring you have at least one person sponsoring you in the India office (ideally someone who worked with you on a project and can tell everyone that you are the best), you start going through the formal process of relocation
I hope this was useful. Good luck!