LSE international relations requires 'A strong set of GCSE grades including the majority at A (or 7) and A* (or 8-9)' so having 3 B's in general might be a setback.
Personally, I was rejected from LSE for history, even with a 9 at GCSE, and predicted A*AA (A in history), due to my personal statement being weaker. LSE is obviously very competitive, but you might have a chance with your current grades and if your personal statement is good enough. I think it's worth a shot, as long as your other options are realistic.