You shouldn't be able to /empty/ your hot water cylinder through a hot
tap, let a lone a cold tap.

I must ask why you think this, If the main stoptap into the house is turned
off as the OP stated and a hot tap is opened then the cylinder would
eventually empty (apart from the dregs in the bottom), unless my
understanding of gravity is wrong!

I've been googling to find out exactly how it should work, it appears to
me that the hot water exits at the top of the cylinder, while cold water
enters the cylinder at the bottom. So the only way of actually draining
a hot water cylinder completely would be out of the cold-water inlet.

Some of the diagrams I've seen seem to have a figure like "--|--" which
looks like a non-return valve to me (and the "" is an expension valve):

Mains -- Press. reducer -- T to cold circuit --|------ cylinder

So my suspicion is that the non-return valve is broken or missing, would
that typically be part of the cylinder itself?