first of all, thank you very much for your reply! Where did you apply?
Following your suggestion I scheduled a Skype chat with the a Faculty member of the LSE programme for today at 14,30 UK time. I'll ask her when to expect my official offer and some other info about the programme. Also, I'll ask if she knows something about the conditions in the offer, because if these are the normal entry condition then everything should work out, but if these are more restrictive it might cause me some problems!
Since this situation applies to you as well, I'll keep you informed of her answers.