In Gr. Britian, it was a confluence of happenings that brought the end.
First, GB never got to the point where we were. At the worst, they were about where we are now with about a 60% circumcision rate so it was less of a committment to give it up. Second, GB was trying to recover economically from WWII which was financially devastating and third, there was a research paper written against circumcision that put the elements in motion.
I suspect that by the time it had happened, the circumcision rate was on a short downward trend because of WWII. After the war, it could have gone either way. All of the elements were in place. It was considered an "upper class" thing to do, it was common and accepted and the medical profession encouraged it. The one thing going against it was the public health system. Britian's economy was devastated by the war and the government was in survival mode. They were cutting every unnecessary expense anywhere they could find one. It wasn't until 1949 when Gardiner published his research project showing absolutely no benefit from circumcision that circumcision was even on the radar screen. However, it was enough for cash strapped England's government to end the government's participation through the public funded health system. While the citizenry could still circumcise, it had to be paid from their pockets and money was extremely tight in post war England. So tight, that many parents simply couldn't afford it. The fact that the public health system didn't pay for it any longer was enough justification that there were no significant health benefits or they would have continued paying for the potential savings. Even for those who could afford it, there was a reason not to. Plus, the fewer parents circumcising their sons would make those who did something of an oddity.
After that 10 year period after the war when the economy revived, it was clear that there was no benefit to circumcision and it never got started again.
I don't see an economic disaster or universal health care in our future so the same elements that worked in England won't work here. We're going to have to find our own silver bullet. That silver bullet is probably going to be the same as for most of the rest of the English speaking world and that is educating parents and medical professionals.