If everything goes well, that connection should be fine. As others have said, it won't take much of a disruption to wreck it, and those kinds of small disruptions are sadly pretty common...

Have you looked at the train? Including the sleeper? Taking the sleeper down the night before is a pretty good price if booked a long way off, saves a night's accomodation, and you'd have several hours in London to see the sights / work before heading to Heathrow. An Advanced Purchase ticket on the train down in the morning might well be an option too