When you say "broken" what do you mean tamaris? Not igniting or starting up, or not heating water or rads. Has anyone been to service or diagnose the problem, someone who is qualified to do so? It may just be the control system, ie timer, or pump, or motorised valve or something simple.
Had my handyman out yesterday who turned up the pressure as it was low but still nothing , he said I needed an engineer. I was thinking maybe best to get a new one
tamaris if the boiler is firing up it probably isn't the boiler. As you run the hot tap do you hear the boiler fire up? You may pay hundreds for a new boiler and not require one.
You could try this tamaris if the water is running cold although the boiler is burning.Turn your hot tap on and then feel the heating pipes under the boiler,if they are getting hot it will be the divertor valve thats at fault. Also just run the tap and go and feel if any of the rads. are warming up, if they are again the valve is chief suspect. You also say that you have had someone to pressure up the boiler. Is it constantly losing pressure? If so you may have a leak. Or did you not check the pressure guage on a regular basis?
In my experience one can depend on British Gas, as otherwise you are in the mire of hoping to chance upon a plumber who is worth the title. A bit like every other trade really, only those who are trying to do too much and failing, and those no one wants to hire, are available to come out and quote.
Update, After much thought and many let downs I have given Vokera a call for one of their engineers to come out, I am prepared to pay the price to get it done without any more messing about.