From the BA website:
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.
In one respect, I would think that “government-issued” IDs (passport / driving licence) are required - but the “under 16 years” note could make things difficult! However, that would probably relate to children travelling with an adult.
easyJet outline other types of ID acceptable for domestic flights. A 3822 is NOT a valid armed forces identity card…
Flybe’s list is even longer!!!
Check with the airline - & if they say yes (I would be very surprised), check a second time - & get the answer in writing!!