You shouldn't be worried... I had BBCC at AS when I applied and got all 6 offers:
Manchester: AAA
Liverpool: AAB
Sheffield: AAB
Leicester: AAB
Lancaster: AAB
Keele (law with business admin- drop business in last yr and u dont have to do a conversion!)- 320 points.
I didn't do LNAT either. My teacher wrote how I was going to do some resits in my reference, and didn't mention UMS. After resits and A2s I had my AAB and got into Liverpool, it's great! So basically, don't worry too much, you shouldn't have a problem. xx