Very interesting. Thanks for your patience.OK , the taps you have linked to, if it was me making the determination, unfortunately are unsuitable.
If you are on a 2 level house with standard height ceilings (~2m) with the cold cistern (CWSC) in the attic ~ 1>2m above the level of the bath taps then you have ~ 0.1>0.2bar pressure in the bathroom with ~ 0.4bar in the kitchen.
The bath mixer tap linked to has a ceramic cartridge and will perform poorly with gravity Hot water judging by the quoted figures
The Sink mixer isn't a dual flow tap therefore there could be issues with the mains cold interfering with the HW supply, that and the min flow figure would suggest poor performance
The basin mixer tap, as was suggested by @HERTS P&D, isn't suitable for the basin you have. You would usually have to change the basin to suit a monobloc tap, that being said, again the choice is a ceramic cartridge type tap that will struggle with a gravity supply.
I would also be surprised if the basin cold was mains fed as usually in these cases all the bathroom water would be supplied from the attic cistern rather than a mains supply run to the bathroom just to supply the basin.
If you search for dual flow mixer taps you will see what is available.
Yes, cold tank in the attic, hot tank on the first floor, kitchen and bathroom on ground. Standard-ish ceilings.
The bath tap currently has two ceramic quarter cartridges - but the new tap would perform worse? That's a shame, I thought they looked pretty similar.
Kitchen sink mixer - I see, about the dual flow. Are most modern kitchen mixers single flow? There don't seem to be many listed as dual flow, and it's not a filter for the Screwfix webpages etc.
Basin mixer tap - is it (just?) about the size of the hole? And again, I am currently using two quarter turn ceramic glands and the flow is fine, but is the flow worse with a ceramic mixer?
The joys of an old house... Thanks again.