Hot water goes off when cold tap turned on

its soo hard to tell without actually being there and inspecting the installation but … if you have a combi boiler and a mixer tap the cold pressure may be transferring through the body of the mixer tap rather than coming out of the spout therefore pushing cold water back up the hot pipe...thus not triggering the flow switch in the hw side of you combi boiler. assuming the tap has isolators underneath you can test this by turning the hot one off and then opening the cold tap and see if the problem persist. if this is the fault an easy fix would be to fit a single check valve on the hot pipe into the tap to prevent backflow. another thought Is that the mains water pressure may not be adequate and therefore has not got enough power to push up to the combi boiler and come back as hot water whilst the tap is running below. You can test this by turning the cold tap on then trying the hot and then slowly closing the cold to see if there is suddenly enough flow to get the boiler to kick in. hope this helps, regards Benji

Try and take the end off the mixer tap and see if there is any dirt etc in it. There is often a round cap mesh filter on the end. It should have machined slots either side where you can turn it with a spanner. Has to be the tap though. The boiler doesn't know where the water is going.

I would get a new boiler fitted

You could try fitting a water arrester on the cold main. That may help