Hot water runs out for 10 mins then comes on again?

It is most likely that there is a partial airlock in the pipework or when the supply to the water heater is being limited somehow.

Hi, this definitely sounds like you have an air lock in the system, The main cause of an air lock in pipes is when pockets of air are trapped by the flowing water, preventing the free flow of water. Also, cold water pipes have less pressure compared to the hot water pipes, as a result, it’s mainly hot water pipes that are affected by airlocks. The pressure in the hot water pipes doesn’t force the blockage out, The water sputters out even when you’ve opened it all the way. The air lock in pipes problem mainly occurs in hot water bath tabs. You’ll notice the cold water is running smoothly but the hot water is flowing sporadically. For a quick DIY fix You'll need a small hose. Connect it to the problematic hot water tap, and then join the hot and cold water tap together. Tie a knot on both ends of the hot and cold water tap with a clip to ensure it doesn’t get loose.Turn on the hot water, then cold water, for about a minute. Turn off the cold water then hot water tap. If the air lock in pipes is still on, repeat the process about two to three times. It should become better eventually. Hope this helps.

It's most likely an airlock caused by potentially poor pipework on low pressure systems Or The main storage roof tank cold feed to the cylinder could be partially block but only letting some water through to the cylinder, after a few minutes of filling the pressure builds back up letting more water flow to the cylinder.

If you have a open-vented cylinder, l think this could be your ball valve that not filling your storage tank up quick enough to fill up your bath with hot water, it's the weight of the water from your tank that push the hot water from your cylinder through to your taps. Or it could be lime scale?