The aircraft probably aren't sitting around in DOH for hours on end just to operate to CWL & EDI, they're probably inbound from someplace else and on a standard turnround.
But hub & spoke timings might have something to do with it, no point departing DOH, let's say, an hour earlier if it can't collect the inbound to DOH connecting passengers.
And some airports have night curfews, I don't think CWL does but how about EDI?