UK friends please help me find my Fiat 500

Have you tried https://fiat500club.org.uk/ or https://www.fiatforum.com/ or https://www.fiatmotorclubgb.com/ ?

 

Unfortunately, CarFax did not begin tracking cars before the late 1980s but it still might be a long-shot try if an owner somehow purposely opted into their system. You never know without trying.

If the car were newer, it might be on CarFax (or whatever the European equivalent may be and when they began tracking). Any hits would give you additional clues where the car was/is hanging out for maintenance, etc. that the service happens to report.

 

Fill out Option B on a V888 form and send it to the DVLA - it will cost you a fiver

https://www.gov.uk/government/publications/v888-request-by-an-individual-for-information-about-a-vehicle

Because of data protection they may refuse but you never know. I would imagine its worth sending photos of the car to prove it has been in your posession in the past.