It will depend on how many places are filled by people meeting their conditions, which can vary fairly wildly year on year. Only if enough people miss their offers that spaces open up on the course will they start looking at who they want to take out of the "pool" of those who narrowly missed their offers.
I have no idea how IB measures up against A-Levels, but the problem you may face is that it's not uncommon for folk applying to places like LSE to do 4 A-Levels - so even if they missed their offer by a grade, they may have a whole other A-Level to their name (if their offer was A*AA and they got AAAA or AAAB or something), which might give them an advantage despite the point at IB not mattering as much as the grade at A-Level. In the end, how the uni judges the value of different systems and such is up to them.
In other words, your situation isn't hopeless, but there is absolutely no way of predicting the "chances" of you getting accepted anyway at the moment. I wish you the best of luck, though!