Hi Max
Yes you can get a new boiler even if your existing boiler is working. A few years ago that might not have been the case. I know when we first had Warm Front round to us they said as our boiler was in working order we didn't qualify and would have to wait until it broke down.
Three years later it was still working perfectly well but we had Warm Front send round a surveyor and they told us we did now qualify, so I'm not sure what has changed.
Our old boiler was about 25yrs old and although spare parts were available to a degree it was pretty much past it. A few weeks later we had our new boiler installed and we also got a new hot water tank which is great as it's one of those that is already lagged, so keeps the water hotter longer. Another good thing was the new programmer which has much more flexibility than our old manual one and it means we can just heat the water for a couple of hours a day but keep the heating on for longer if needs be.