From their own website:
For 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.
From my experience, most time they won't ask for an ID, but some times it does happen. Few times it has been done at random to certain passengers by the gate agents.