How many people can count a Hollywood A-list actor as their neighbour? Well, not many at all.

Take Johnny Depp. There’s the people who live underneath his flat in the Paris suburbs, his neighbours over the way at his South of France bolthole and, more recently, new locals to get to know at the Norfolk mansion he bought near Burnham Market.

But neighbours of a very different kind are to be found near his home in the Bahamas. And that’s because they need a boat to pop over for a drink – Depp and long term partner Vanessa Paradis own one of the area’s many islands, Little Hall’s Pond Cay, and the neighbouring cay is currently for sale.

It’s in the central Bahamas and on the market for $75 million – although smaller and less developed cays are currently for sale at around £10 million but often with strange names.

For example, some rather alarming monikers recently on the market have included Cockroach, Bottle and Goat Cay ranging from £1.1m to £25 million in price.

But the buyer of this private island gets more than just a patch of beach and a few palm trees. Its 38 acres include a large plantation-style manor house, separate fitness centre, infinity pool, a working lighthouse and a staff village for 29 people.

There’s also a heliport, deep-draft docks, freshwater treatment plant, beach cottage, harbourmaster’s house and twin guest cottages – all accommodating 22 people in fairly lavish luxury.

And if you’re wondering how you get there – the nearest main island, Exuma (after which the group is named) is some 60 miles away. The answer is, this island comes with its own seaplane.

But get bidding fast. Depp and Paradis are said to be having relationship troubles and so you neighbours may soon drop down to one, rather than a couple.

For more information, contact agent Sotheby’s International.