The Jimmy Cagney movie "G-Men" was released in the United States on May 4, 1935. If business held true to form when it came to overseas distribution, then it probably began playing in the UK six months to a year later.
Hercule Poirot and his friends Captain Hastings and Inspector Japp went to see the movie (of which Poirot highly disapproved) in the 'Poirot' episode "The Mystery Of The Cheap Flat". As the theater seemed to have full attendance, I think it may have been close to the date it opened in London.
The people seen in the streets in this episode are always bundled up, and yet there is no sign of snow. Therefore, I think "The Mystery Of The Cheap Flat" may have occurred in November of 1935.
Alas, the IMDb.com, as well as other sites, failed to produce a date for release of "G-Men" in Great Britain; so that's the best I can narrow it down.