You only need to fit a check valve on the mains in. Check to see if there is already a NRV fitted near the stopcock or if you have a softener fitted -this usually has one incorporated. If yes don't fit any more.
If you don't have a check valve already fitted somewhere in your cold supply, then you must install one if fitting single outlet mixer taps. The check valve should be somewhere in the high pressure cold supply. Because it is in the high pressure side, it will not affect your low pressure hot.
Fitting one in the hot side to prevent back feed up the hot, is a little more tricky. I have in the past dismantled a check valve and removed the spring, just leaving gravity and back flow to operate the check. Generally though, they are not required in the hot feed. Just remember, if you open the tap in the centre position full bore, cold will be forced back up in to the header tank.
Strictly according to the Water Regulations you need to have some mechanism on EVERY appliance (which includes taps) to prevent syphonage.
With a basin tap you have an airgap which is an acceptable mechanism.
Although SBs advice is not iaw regs on a practical level he is not wrong in respect of baths, showers and taps unless the shower head can be dropped into water - say in the bath - where one is required. A single double check valve fitted downstream of your stop c o c k is normally sufficient even though the Water Board could be nasty as not complying if they really felt like it.
Water softeners, dishwashers etc should always have their own fitted.
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