I’ve seen the term ‘British’ vs ‘USA’ sound used quite regularly for guitar amps.
I think it perhaps goes back to the valves and (limited) components that were available here in the 50’s and 60’s vs over in the USA.
Guitar amps were designed using EL34, EL84 power valves, vs the 6V6, 6L6 etc.
The transistors (which would have been germanium) available over here were also different to what was available in the USA.
Many of the circuits/designs used were based on similar principles and reference designs (found in the old RCA/Mullard Technical reference books etc.), but due to the components used, produced very different sounding circuits.
A lot of the British early guitar amp designs etc. were based around US designs and schematics (one of Marshall’s early amps is pretty much a Fender Tweed Bassman clone with some component and valve changes).
When Rock N Roll came along, everyone wanted to sound like the USA artists that were around (Elvis, Buddy Holly, Chuck Berry etc. etc.). The Beatles changed all that of course when they came on the scene (though I don’t think they changed the popularity or aspiration to own American musical equipment over here).
My Dad played in bands in the late 50’s (inc. a Shadows cover band ) and he said that everyone wanted the USA stuff, particularly Fender, but nobody could either afford or get hold of it (certainly not in Sheffield . ).
Most of the UK and EU stuff was considered (perhaps wrongly) as being inferior.
Having a Fender or Gibson guitar or amp back then was very rare.
So they had to make do with what they could get hold of.
I think a lot of the UK/EU musical equipment manufacturers picked up on the American Rock N Roll boom and tried to cater with their own clones, or at least designs heavily influenced by the American manufacturers, using the components that were available to them.
Through these different components, design changes etc. came a lot of equipment had it’s own character and sound.
I think this is partly what then lead to the ‘British Sound’. … ironically a lot of equipment that was heavily influenced by American designs!