as for the uk train stations, the temperatures are in part due to their age - London Underground was built in 1870s, and since that time rocks accumulated so much heat that it is extremely difficult to maintain human-friendly temperatures. Japan subway is 70 years younger, so it’s easier for them to maintain temps.

(And my hometown Warsaw subway is even younger - 50 years, and we don’t have AC whilst temperatures are at a perfect level).

What London underground might need is not AC, but a process to cool down rocks - importing coolness during winters. To maintain equilibrum you’d need to pump out around 1TWh heat every year. To bring it down to normal levels in say 20-30 years you’d need to pump out 2-5TWh a year.