My En-suite basin cold tap does this also. It is because both hot and cold
pipes are close together under the floor so the heat from the hot pipe heats
up a short section of cold pipe and therefore the water inside.

I was thinking that at first but it doesn't matter which tap I run and
it happens even when the central heating is off and I haven't ran any
hot water taps.

And if I turn off the water at the mains and open a cold water tap, the
water from my hot water tank eventually drains out through the cold water
tap.

Have you actually done this, i.e. EMPTIED the hot water cylinder via a cold
tap? Sounds a bit strange and costly IMO.

Yep. If I were to want to do a plumbing job on the cold water side these
days, I'd have to turn off the water at the mains, open a cold water
tap, and wait for the content of my hot water cylinder to have drained
through the cold water tap. Bizarre and annoying...

Shouldn't there be some kind of non-return valve ensuring that the hot
water doesn't drain back into the cold water side???

Are your taps in question mixer type or two individual pillar taps?

They are individual taps, apart from in the kitchen which is the usual
mixer. Doesn't matter where I experiment, same result :-( ...