Found this remarkable property on the Isle of Rum, off the coast of Mallaig, Highlands. Rum is one of four small islands; Eigg and Muck I've visited but not Canna or Rum.
https://www.rightmove.co.uk/properties/168906884#/?channel=RES_BUY
It is only o/o £750,000 and includes 18 acres of land and all contents (incl a Steinway piano) but has imo a number of challenges not least that upgrading requires importing huge amounts of materials, not easy. Particulars state that around £10million needs spent. Additionally, the Rum community requires a written statement of potential owners intentions with the property.