"Fly with British-registered airlines employing British-based crew"
There's plenty of choice -
Thomson
Thomas Cook
EasyJet
British Airways
Monarch
FlyBe
Virgin Atlantic
British Midland
Between them that little lot will get you virtually anywhere.
In general, on time, using properly-maintained aircraft, operated legally, according to well drafted procedures and for a price most can afford.
Sorry, that was me just being positive