i had the same problem a couple of days ago. central heating working but no hot water from the taps.
After some troubleshooting, i decided to bleed the rads in the house. The Ground floor rads had no air in them and were fine, but the ones upstairs, closest to the boiler tank had air in them.
As soon as i let the air out, the boiler tank in my bedroom started to feel hot, indicating that the inside coil was receiving hot water.
So in this instance, there appears to have been too much air trapped between the bath radiator and the boiler tank, which was stopping the hot water from reaching the boiler tank.
Have a go at bleeding your rads first, before undertaking anything more complicated or labour intensive.
Istak
October 2015