Badge dates
Mayfair production started in late 1982, so if it's a Y or later it could well be a Mayfair.
Mini 1000 production ceased in 1980 as it was replaced with the HL and then HLE.
As far as I can remember the only place early Mayfairs actually said Mayfair was the boot lid and the rear quarter panels. If you have a bootlid that says the car is a mini 1000 and the quarter panels say you have a Mayfair then either you have a Mayfair that has had the bootlid replaced or a mini thou that has had Mayfair decals applied.
There is an outside chance that it's an earlier car reshelled into a Mayfair.