All airlines require some form of ID, but the rules vary.
easyJet fly from Glasgow to Gatwick, Luton and Stansted. They accept any form of photographic ID, such as a bus pass (as well as more 'official' documents, such as a passport or photo-style driving licence).
bmi fly from Glasgow to Heathrow. Unless you've got a police warrant card or an armed forces ID card, they'll only accept a passport or photo-style driving licence.
BA fly from Glasgow to London City, Gatwick and Heathrow. They only accept a passport or photo-style driving licence.
Ryanair operate from Glasgow Prestwick to Stansted. They also only accept a passport or photo-style driving licence.
Chris