Boiler 'tripping out' as though overheating

Recently, my Gulfstream 2000 central heating would only stay on for a few minutes before the overheat sensor popped out and cut off the system. Using my Homecare agreement with British Gas, I summoned an engineer who informed me it was the heat exchange and I should get a new boiler fitted (it's only 6 years old and serviced from day 1) and here are our prices etc etc etc. I'm not convinced by the swiftness of BG to press for a new boiler (helped by the knowledge that they hate going out to work on Gulfstreams) and now, I notice that the overheat sensor reset button just pops in and out like a switch whereas before, I could press it in and it would stay depressed until it overheated or whatever it was doing. Does this sound like a new boiler fix or, should I be looking at trying to fix the problem with new heat exchange and power flush?

PS I simply don't trust British Gas and think they may be trying to rip me off!