British soldiers in the series continually refer to "The King's Royal Army" or "His Majesty's Royal Army". Serving British soldiers would not refer to the Army in that way. The Army is simply "The British Army", not the "Royal Army".
The British army show up several times during 1937 using Jeeps. The Jeep wasn't developed until 1941. In 1938, Zacks shows off his MG TD, a car that wasn't manufactured until 1952