From the BA site:Identification on UK domestic flights
If you are flying solely within the UK, including Northern Ireland, you do not need a passport but we advise that you carry photographic identification with you when travelling, such as your passport or driving licence. This may be requested at certain points in your journey. Children under the age of 16 years do not require identification to travel within the UK.
Edit: Appreciate that wasn't an entirely helpful response! I'd call BA and ask them.