Sounds like the diaphragm in the diverter valve. If the boiler doesn't fire when you open the hot tap, it will be the diaphragm. You'll have to get a Corgi registered engineer out to replace it. Do not let him make you change the diverter valve as this will be uneccessary and more costly. He shouldn't charge more than £90 to do the diaphragm.
Joe from AOC Plumbing & Heating Services, February 2006