Very old news. This claim of Ken Wood's has been much discussed in the past. He may well have been physically capable of running sub 4 - although by 1954 his competitive performances hardly support this claim - but there is absolutely no evidence to support his claim. Who timed/witnessed the sub 4 run? Has this person ever come forward to support the sub 4?
Silly story, really. Bannister did run the first official sub 4. And, reference to other posts on this subject, it was not something that only Brits bothered about. Landy and Santee were chasing the goal in Australia and the US, Hagg and Anderson chased it in Scandinavia in the 1940s. It was a worldwide thing.
Of course, if the 1939-45 was had not happened it is quite likely that the barrier would have been broken before 1954. Gerschler had an athlete - Harbig - run 1:46 for 800 in the 1930s and most people would say that thie time is more impressive than 3:59 (?).