Neither country had a significant conception of the handgun as much more than a badge of rank in military usage, nor were they common features of their civilian society since before the invention of the revolver. Whereas the USA has had an abiding societal awareness of the desirability of handgun possession [note I did not indicate "need" or "ownership;" those are separate issues] leading to the US exporting revolvers the world over, and in turn importing semi-auto pistols in large numbers since they were invented, as well as developing our own varieties.
Ultimately, at the time that semi-auto handguns were proliferating and concerns for their manufacture were becoming established, England and France had bigger matters to attend to, and as a result, it was easier [in the case of England] to adopt the successful designs of others [BHP] and farm out their manufacture to other members of the empire [in far off Canuckistan, via John Inglis [sp?]] or in the case of France, waste a lot of time developing their own oddball designs to be built at one of the state-owned arsenals [Chaterrault, St. Etienne, & I forget the third, the "B" in MAB] because, you know, they're French & have to be "speshuul..."
:banghead:
Seriously, the US lucked out: because of our peculiar societal development, we ended up w/ John Browning ["St. JMB", mechanical genius & patron saint of gunfire
] who developed the vast majority of successful semi-auto pistol designs once Borchardt, Luger & Mauser demonstrated that it was indeed possible to make a salable product. In the world of semi-auto handguns, pretty much everything since JMB's turn at the wheel has been mostly derivative of his designs [one of the reasons, JMB held Pederson in such high esteem is because he [JP] had come up with a pistol [the R51] that functioned on a principle that JMB apparently had never considered [& therefore had no patents covering it.]] CZ 75? Derivative. Glock? Derivative. And JMB, being the genius that he was, patented his designs in both the US [where he typically licensed production to Colt] and abroad [where he had a sweetheart deal with Fabrique National of Belgium, now FNH [FN Herstal.] So except for Soviet Russia [which did not respect patent law & stole vigorously from the West: the TT33? Derivative!] that largely wrapped up the market for the 1st half of the 20th century. And it all just follows on from there.
Your question seems simple at its face, but the reality is that the full answer is a detailed study of firearms history & economics of the 20th century. Get reading!