"It's called the Kestrel - until we come up with a better name"
The plane is clearly intended to be the Spitfire. When Mitchell designed the Spitfire, he called it the Shrike. He thought "Spitfire" was a silly name.
A prototype of the German Messerschmitt Me-109 fighter plane actually used a Rolls-Royce Kestrel engine.
Based on the short story of the same name from "Murder in the Mews" (1937)
At the end of the episode Poirot, Hastings and Japp drive off in a 1931 Lagonda registration plate GN 8258. This car is still in use, latest log book (V5) issued on 21 March 2012 and currently road taxed March 2021, renewal due 1 March 2022.
The "Kestrel" is a kind of hawk, more specifically a small falcon.