Brian,
There was a RAF Commands thread dealing with Autogyros/Rotas in France here:
https://forum.rafcommands.com/forum/...ight=Avro+Rota
Also, the Aeronavale appears to have used their autogyros for coastal surveillance (incl. mine search) from Feb. 1940 on in the Channel area, but the craft were pulled from service, forming too great an easy prey.
The Russians had their Kamov A-7 types, in Japan the Kayaba Ka-1 and Ka-2, the USA the Pitcairn OP-1, XOP-2 and Kellett KD-1 (Y/XO-60) and in Germany the Focke-Achgelis makes.
Also, the RAF tested the Pitcairn PA-39 with deck trials from the ship Empire Mersey in American waters in May 1942. They ordered some (BW828-834) but not sure if any ever made it across the ocean.
Especially the Russian and Japanese autogyros saw active service.
The RAF Rotas were extensively used in No. 529 Squadron for radar calibration duties across the country.
Leendert