Ah, lovely! You should apply to Bristol.
No, seriously, their law program is actually quite good!
The OSSD isn't similar to A-levels, actually, haha. It's similar to the US high school program, in some ways? It's very different from A-levels, though. I had a friend in IB (who also applied to some overseas unis) who mentioned he had taken some classes that are also offered in the OSSD. So I think it's more similar to IB than A-levels.
In any case, I would recommend you submit your IB marks. Since it's an "international baccalaureate" it's recognized more easily across the world. However, I did have someone who mentioned to me anecdotally, that IB offers are sometimes higher than those at the diploma level. I can't compare with that, or say whether that's really true, but it's your choice.
In my opinion, the IB will probably give you more offers, but the BC diploma will probably make it easier to achieve those (possibly fewer) offers you receive. It's really your choice. If you're doing very well at the IB, I definitely suggest the IB.
For Canadian certifications, I emailed my unis and asked for the Canadian OSSD equivalent, which should be similar to the BC equivalent. I suggest you do the same. They're fairly prompt and friendly. Send them a nice email with the phrase, "I'll be applying for Law for 2013 entry at [your uni]. I am doing the Canadian BC diploma. What would be the equivalent grade requirement?" with some "please"s and "thank you"s in there. haha
In very broad terms:
A*AA-AAA is an average of 90 or higher to have a good chance at getting a place
AAA is an average of 85-90 (or higher, obviously)
AAA-AAB is an average of 80-85ish
Of course, depending on some circumstances, and prior performance, some of the smaller unis may give you lower offers because they know they want to give you a place... you know? For example, even though RHUL has an AAA-AAB typical offer, which would translate to a conditional offer of 80% or higher, their condition to me was a "pass" which is only 50% or higher.
Granted, the unis that do this are probably not the unis you want to attend...
Finally, if you're using the BC diploma, I think you choose 5 out of your 7 Grade 12 courses, right? For regular Canadian unis?
Well, the conditions that the UK unis give you will be exactly the same. For example, in Ontario, we need 6 out of 8 (or more) Grade 12 courses to use for Ontario uni applications. My offers from UK unis were, "An average of 80% or higher in six OSSD subjects" or "An average of 85% or higher in six OSSD subjects, including English" English is a prerequisite anyway for the OSSD Grade 12, so they'll do things like that.
Some unis may ask you for a specific subject, e.g. if you were doing Physics they would probably ask for one of your subjects to be maths; however, since you're doing Law, I doubt this applies to you.
ETA: Don't be afraid to ask more questions! I'm also open to questions about the Oxford college/interview/etc. system. Oh dear, didn't this post turn out so very long, though!
Another ETA: Why don't you apply to SOAS? They also have a good ranking and they're in London, which it seems that you like!