BAA could raise their fees by pretty well as much as they wanted to at LHR, assuming the CAA would let them - which they probably wouldn't.
The sad thing is that because the UK is so "London-centric" airlines feel they have to be at LHR, and aren't likely to decamp to BHX / EMA / CWL / BOH and any other non-London airport any time soon, whatever BAA do.
I suggest the situation at LGW might be slightly less clear cut, as the airport is now much more leisure orientated following the exodus of trans-atlantic services to LHR, and as such, more cost sensitive.