As others have said, a passport is not required for UK domestic flights.
However I have reported on a number of occasions that LGW, which has a common domestic/international departure lounge has had temporary outbound passport control checks immediately after security.
The first time was immediately after 7/7 and I happended to have my passport on me and thought best not to make a fuss.
However when the check was repeated about 2 months later, although I had my passport on me, I simply showed by bp and said 'domestic flight'. I was then waived through.
The moral is have some form of photo id like a driving licence, just in case.
However we are still a liberal country and until ID is mandatory, one should make the point that internal travel is passport/ID free (at least until BA's hand is forced like the ridiculous nonsense over hand baggage).