Not much time passes between Season 1 and Season 24 because Topham's children (Stephen & Bridget) are kids in every Season. They age MAXIMUM 4 years or so (from 8 to 12 or something).
Elizabeth II is queen in Season 4 and Season 24 plus her hair isn't really gray yet, so we can narrow the show's placement down to 50s-80s. Her son appears as a kid or young teenager in Season 24, so the window gets smaller to 50s-early 60s.
Kenji gets called a "new invention" in Season 24. In real life his basis was built in 1964. I think all of the other engine's basis also exist at 1964, maybe there are 1-3 exceptions that are just errors.
Also, the Dieselisation in Great Britain was mainly in the 60s.
CONCLUSION: Thomas the Tank Engine takes place in the early 60s. Not many years pass between Season 1 and Season 24, maybe it occurcs from 1960-1964 or so.