No one - not even Sherlock Holmes - would be able to phone the BBC and ask for a specific record to be played on air immediately, in the manner of a jukebox. There were no "BBC request stations."
The opening montage gives a list of the Voice of Terror's broadcasts: Sunday February 5th, Thursday March 23rd, Friday May 12th, Saturday July 1st, Tuesday August 8th, and Tuesday September 19th (actually the day after the genuine Nazi propaganda broadcasts began to be transmitted on radio). These dates all equate to 1939, the majority well before World War II officially broke out on September 3rd of that year.
After a broadcast warning that a train carrying a government minister will crash outside Liverpool the train seen crashing into a gorge, is obviously an American one and there is no such scenery anywhere near Liverpool. Another broadcast about 5 minutes later warns of another crash and there's sounds of an American type train siren.
The Nazis didn't have to transmit "The Voice of Terror" from Germany. They could have used the powerful transmitter from captured Luxembourg, as they did in real life with Lord Haw-Haw.
When they show one of the factories burning along the harbor, you can clearly see a "X" shaped railroad crossing signal in the lower left corner. However, those signs were used in American and not in England where this is set. They must have used some stock American footage of a burning building.
After the Voice of Terror informs the Council of the fire, Holmes discusses that the Voice of Terror is in England, Kitty comes in and tells Homes something. Holmes then leaves without taking his briefcase and notes he brought to the meeting.
When Sherlock Holmes first arrives during the security council meeting he can be heard saying "Gentleman" as his first word. If you look at Sir Evan Barham's lips he can clearly be seen mouthing the word "Gentleman" at the same time as Holmes, but only Holmes can be heard saying the word.
England's south coast looks unusually mountainous.
When Holmes and Watson first meet Meade, his name is never stated, yet they know it when they discuss him in a scene shortly thereafter.
At c.41 minutes, Holmes is clearly miming when he plays his violin.