If you are already checked in (OLCI) for your BA flight, AND you can get DL to interline (through-check) your checked baggage, then you should be able to follow signs for Flight Connection Centre and do the regular in-transit without exiting and starting all over again. It's a bit of a PITA to change terminals landside outside of the secured system versus going via FCC.

If you don't have your boarding pass for BA, there are check-in desks in the Flight Connection Centre, but the BAA security check may not let you through. I have been able to get through showing my e-ticket and they let me check-in in the FCC but I had hand baggage only.

Best bet - do OLCI for your BA flight, have your BP, get DL to through-check you bags, and you can stay in the Flight Connections system at LHR and do an airside transit from one terminal to another.