BA's site has a summary of requirements for their flights and also their franchise flights (Comair, GB Airways, Loganair, Sunair of Scandinavia)

The Department of Transport lists the UK airports where the one-bag rule doesn't apply any more; travellers flying out of any airports not listed there can only carry the one bag. I believe these airports include Gatwick, Jersey, Newquay and Luton - I've not managed to find a complete list.