BMED is probably the only airline based at LHR these days with there own Flight Ops Control department... (Currently they are looking for an Operations Co-ordinator - Admin based)
Sadly BA, is a closed shop and can only get opportunities through internal applications. So you would need to join BA first via Checkin/Cabin crew etc...
You could try getting into dispatch rather than Ops which may open a few doors for you..
Aviationjobsearch is also a good site to watch......