Due to cold weather (I presume) when I turned on the tap yesterday no hot water came out, even though heat was on for hours and immersion tank was hot. But cold water was running fine. After a half hour hot water started running, but today same thing happened and this time hot water did not start at all.

What is the cause? If it's frozen pipes would we have any running water at all? And surely we should have been able to use water from the immersion anyway?

Due to cold weather (I presume) when I turned on the tap yesterday no hot water came out, even though heat was on for hours and immersion tank was hot. But cold water was running fine

You may find this article interesting.
Can hot water freeze faster than cold water? (http://math.ucr.edu/home/baez/physics/General/hot_water.html)
Good luck, Tom