This has actually happened to me on an EasyJet flight from RHO to LGW last year. The incentives were that a Greek ATC work-to-rule was about to start, and the inbound was 20 min early. I never knew whether this was because they'd done the same thing at Gatwick or because of tailwinds, but the ground staff shaved another 5 minutes off the turnround and the plane started to taxi 25 minutes before scheduled departure (no airbridges at RHO, and no pushbacks required). On this occasion the loads were very light as it was early April, and nobody was left behind.
so Easyjet do leave early when it suits them, and they can get slots.