I'd have no hesitation flying them (and have used them quite a few times) - they're one of Europe's largest and most successful airlines, and are generally well thought of.

What does concern me, though, is your long-haul connection (or "non-connection", seeing it's on separate tickets). How much time are you allowing for this? And have you checked it's the same airport? (Most long-haul flights depart from LHR. Easyjet uses several other London airports but not LHR). Their punctuality record is OK, but if I had a long-haul flight to wouldn't book a same day (non-) connection on separate tickets.