All airlines insist that some form of identification, BEARING A PHOTOGRAPH, is produced for all internal flights. (They're obliged to do this under anti-terrorism regulations). The actual form of identification which is acceptable, however, varies between airlines. Most carriers (e.g. Ryanair) will only accept a passport or EU driving licence. The Belfast to Luton route, however, is operated by easyJet who are sometimes a little more flexible.
If you think that you've got some form of PHOTOGRAPHIC ID , which might be acceptable to easyJet, you should phone 0871 244 2366 to check. If the person who takes your call says that it's OK, be sure to get their name and then arrive in plenty of time at the airport. This is because there have been people who've been told, on the phone, that their ID is acceptable, who've then had problems at the airport.
Chris