There is only one.
They do it everywhere, there's always a rare one of each colour, but obviously Mayfair is the rarest with only ONE ever.
With the other properties you get 2/3 of the colour and assume you're close, only to find out that everyone only has those exact properties too.
Sorry to be the killjoy.
Edit: Park Lane is very common. If by some weird coincidence someone had Mayfair, they'd have Park Lane already, or could buy it for about 30p from eBay or something.