When running a bath, the water will get very hot for about 5 secs, then cool off again. If I turn off the tap, then back on again, the same thing will happen. We have planty of hot water everywhere else, including the shower and sink next to the bath. Any ideas?
It sounds as though you have a combi boiler, and the bath tap is restricting flow to a level below that which the boiler needs , in order to sense "hot demand", and fire up the boiler. In this situation you will only get the boiler-charge of pre-heated water, about 13 litres in my unit.
If the tap has not been renewed recently for the wrong type, it may just need a new washer to boost flow, enough to fire-up the boiler.