Be a castaway every day of the year – Taransay island was the setting for the original BBC series and is on the market for £2m

A beautiful Hebridean island, made famous by the reality television series Castaway, is being put up for sale complete with spectacular white beaches, a private herd of deer, wild otters, trout and seals.

The uninhabited island of Taransay in the Western Isles has seen pagan Celtic settlers, a massacre involving warring medieval clans and in 2000, a group of 36 city dwellers and a large television film crew trying to survive unaided on the edge of the Atlantic.

That BBC series, which made a star of one equally rugged young castaway, Ben Fogle, but upset others who took part, transformed the island from a secluded spot for the hardiest and best informed travellers into one of the Hebrides' most famous private islands.

Made up of two treeless, cliff-fringed and wind-battered islands connected by a wide, sandy isthmus, Taransay is being sold by its owners, Angus and Norman MacKay, two locally-raised brothers who live on the neighbouring island of Harris, for offers in excess of £2m.

With a history of habitation stretching back to at least 300AD, Taransay was bought by their father John MacKay in 1967 for £11,000. It once had three villages but the last family left the island in 1974, leaving the properties derelict and a place mainly for sheep grazing, and intrepid travellers.

When it was selected for Castaway, several houses were upgraded, leaving three – the farmhouse, the old school chalet and a more basic bothy with beds for 10 – for the MacKays to rent out as self-catering holiday homes.

They have only rudimentary services, but some of the most spectacular sunsets over the Atlantic and sunrises over the sharp-peaked mountains of Harris immediately to the east.

The island, thought to be the largest uninhabited island in Scotland, is being sold in its entirety with a working sheep farm – currently at 680 breeding ewes – and with 200 red deer, its holiday homes and an offer from the MacKay's to sell a landing point on the beach on South Harris for its new owner to pull up and store the boat required to visit their property.

John Bound from estate agent CKD Galbraith, which is selling Taransay, said the sale was quite rare. At 3,445 acres Taransay is unusually large to be sold in its entirety. And the MacKays – one a farmer, the other a business man – are selling up for pragmatic reasons, he said.

"The sale is purely a business decision; it suits both families now, the timing and everything," Bound said. "It's quite unusual to get an island of this size where everything is owned. Usually something has been sold off or is crofted. Anyone can now buy it in its entirety."

The firm said the island had the potential to continue as a holiday letting business, but also for its country sports, deer stalking and its fishing. Taransay offered "the country sportsman an abundance of activity whilst protecting the biodiversity of the island, with hill lochs teeming with brown trout, first-class coastal and sea fishing, as well as a herd of around 200 head of red deer providing some enjoyable and sustainable stalking."

The temporary Castaway islanders, watched by 9m viewers at its peak, lived in "pods" in the deserted village of Paible, where they raised their own pigs, cattle and chickens, and grew their own vegetables. They enjoyed electricity, supplied by a wind turbine and a small hydro-electric scheme, and a water supply. Of the original 36 castaways, 29 stayed on the island for the full year. Most returned to their normal lives; Fogle went on to become a television presenter, including for the BBC nature and farming series Countryfile.