Having consulted Management here, it appears that we have regularly gone through Security in both UK and US airports with l/h amenity kits in our carry-ons without even thinking about the liquids rule!! I am advised that she doesn't usually bother to take the BA ones now, but the fact remains we have never even considered that aspect.
OK, most of our US connections have been with TSAPre✓ in recent times ... but we must have gone through LGW [on the way home] many times as 'naughty people'.