As we have unbalanced supplies, it sounds like we need them - but what
is the purpose? To stop mains pressure water ending up in our hot water
pipes, or to stop contamination going back up the cold water pipe from
the hot water?

Personally, I would expect a gravity hot supply through a check valve and a
narrow bored single lever mono mixer to be unacceptable. I would only fit
such a tap on a pumped or mains pressure system. You might get away with it
on a gravity only system with no check valves.

The most important check valve is on the cold water side to prevent
contamination of the mains supply in the event of mains failure.

Mains cold entering the hot system is unlikely to either occur or have
particularly bad side effects. The most likely effect is to overflow the
header tank, but probably not.

The check valve on the hot side will also seriously impact performance, so I
would personally leave it off. If the performance of the hot supply is not
good enough even without the valve, you'll need to look at pumps or mains
pressure hot water systems.

Christian.