True Blue wrote:

Is there any virtue in fitting a pump to the bathroom supply only?

I'm on gravity feed.

If you've got room for a pump in the base of the airing cupboard,

e.g https://www.screwfix.com/p/salamander/2502t

give it dedicated feed from cold tank in loft, and a dedicated feed from
the hot tank using a surrey/warix/essex/tech flange

If you han't got room at base of airing cupboard there are alternative
"negative head" pumps depending on location.