Yes, sockets were a uniquely American invention..
Err...actually no!
The earliest interchhangable socket wrenches I've ever seen were British made and dated from the 1870's if memory serves. They came complete with a ratchet (a red painted steel thing), T bar and even an extension, so were pretty recognisable as the tools we use today. Seem to recall that the drive was an EXTERNAL hex. Manufacturer was Accles and Pollock.
I have British made sockets and handles that are from government contracts and thus dated - earliest of these I have is dated 1913 and is a socket with an internal hex drive. My Grandfather would have purchased this, among MANY other things, as surplus between the wars, so I have no doubt of the provenance! These were still rare in that era of course, when a box of open ended wrenches was adequate for most tasks, but they existed.
Hex drives were fairly standard in the U.K. In size terms, the old British hex drive tools were somewhere between 3/8 and 1/2 inch tools today. These patterns subsequently got changed to 3/8 square drive, which is why British tools were traditionally a bit heftier than their American cousins, if you compared drive sizes!
Of course, there wasn't a huge choice of drive sizes back then. British tools were hex drive or do without, so the really discerning sought out American tools in the then novel drive size of 1/2 inch square, simply because they were bigger stronger tools.
Grandfather (and yes, he did used to discuss such things around the dinner table) was of the opinion that the first 1/2 inch square drive tools to be seen in the U.K. were American. He liked 'em so much he bought a load, and I still have them (Mostly Blackhawk). I think it's fair to assume that square drives were an American innovation.
Of course, other drive sizes followed. 3/8 (I think a Snap On thing?) was called 'Ferret' and this lives on today in their part numbers - 3/8 drive having an 'F' prefix!
Although there was a lot of faffing about with other sizes everyone eventually settled on the sizes we have today.
With some exceptions. Many tools for government contracts, both aBritish and American were made in non standard drive sizes. I have some examples.
In the mid 80's the very first French made Facom tools reached the U.K. I quite liked 'em then (and still do) but while they looked great, all the drive sizes were 'metric approximations' and didn't fit anything else. They subsequently changed that.
Though only recently Facom were at it again with their CDX (or somesuch) drive. Although doomed to failure it was a good idea, and the tools were sized halfway between 3/8 drive and 1/2 inch drive - much like those old British ones!