seeing as hot water to the tap is hot and the boiler has hot water in it and heating is also hot water, i'll call the boilers hot water primary, hot water to the taps, taps and hot water to heating, heating..
if you turn the heating on, the boiler runs, pump turns on and diverter valve sends heating to the radiators..
when you turn on the hot tap, the pump kicks in, heating the boiler, primary pipes (not heating) pump kicks in, fan runs, air switch activates, diverter valve keeping heat within the boiler and the pump sending heat around the boiler and hot water heat exchanger..
cold water at the same time flowing through this hot water heat exchanger.. this keeps fresh clean cold water apart from dirty primary boiler water..
the end result being hot water at your taps.. ive tried to explain as best i could for people too lazy to search google..
i hope ive explained now that if he has hot water, his pump is fine and that the op should ignore other members claims that he should look at the pump when in fact he'd be wasting his time..