Well it was the Americans who got on the bandwagon along with the UK in Victorian and Edwardian times. I believe the UK gave it up faster than we in the US. But mainland Europe didn't seem to ever embrace it in the same way.
The UK didn't really take up circumcision for the reasons that Americans did and it was certainly far more class based. The British upper classes took to it far more readily than commoners ever did.
One of the historical reasons for this was Empire. Britain (and the East India Company) ruled over vast swathes of territory in the 19th century and large parts of this empire was inhabited by Muslims. Trade was conducted in even larger parts of the world with Muslim rulers. And one of the customs so often described in historical accounts in the 18th/19th centuries was that many Muslims of high standing, refused to do business (either trade or politics) with uncircumcised people, It was thought to be very unclean. They would insist (and somehow or another find out) on the circumcision status of the non-Muslim in question. How this was done in practice is not always clear, though it was described in some instances with having intermediary physicians having a quick look and reporting the outcome.
So, in order to keep trade going smoothly and profitably and in order to placate local rulers (remember that India comprised many princely states, independent in theory and ruled over by Muslims whose sensibilities had to be taken into consideration), the East India Company made it mandatory that employees be circumcised. Employment in the EIC was very profitable and vast fortunes were made by members, so they considered circumcision a small price to pay in return for wealth and riches. Soon, with (high class) families contemplating a career for their sons in the EIC or later the Colonial Service, they had sons circumcised at birth.
And even for those who did not go East, circumcision soon came to be imitated as something that the higher classes did, as a sort of status symbol.
Obviously the British had their anti-masturbation obsessed parents and physicians, but not on a scale as in the US and they did not stress circumcision as a blanket solution. They probably knew that circumcised colonial administrators and members of the EIC were just as prone to the vice as any non-circumcised Britisher.
I would think British went the way of cold icy showers and sending their offspring to public schools to be humiliated, toughened up and reared in the appreciation of corporal punishment fetishism ... 😃