When you attract screaming fans everywhere you go, what do you do to get some peace and quiet? You buy an island, of course. That’s what John Lennon did in 1967, buying Dorinish Island, which later became known as Beatle Island, in Clew Bay, Co Mayo.However, it turned out not to be practical for one of the biggest rock stars in the world to commute to gigs and recording sessions from an island off the west coast of Ireland, so he offered the island rent free to a man named Sam Rawle, whom the media dubbed “King of the Hippies”.Rawle set about establishing a self-sufficient community on the island, much to the bemusement of the locals on the mainland, which eventually disbanded in 1972.Lennon told the New York Times he planned to retire to Dorinish and had already submitted a planning application to build a house there when he was killed in 1980. His wife, artist Yoko Ono, sold the island in 1984 and donated the proceeds to an Irish orphanage.Not everyone’s life may quite reach the frenzy of Beatlemania, but the realities of modern life can leave you wanting to retreat to your own little corner of the world. Here are four Irish islands on the market where you could do just that. The property on Innischoragh Island in Clew Bay, Co Mayo Innischoragh Island, Clew Bay, Co MayoPatrick Chambers Estate Agents, €650,000What’s on offer: A 10-acre island laid in grass suitable for sheep grazing, and a home with panoramic sea and mountain views in Clew Bay.Accommodation: A two-bedroom home extending to 108sq m (1,152sq ft) in decent condition, constructed in the 1980s. It comprises a kitchen/livingroom, office space, two double bedrooms, a bathroom and a utility room. It has solar panels for energy, and a backup generator. Water is provided by the collection of rainwater stored in an underground tank, and there is a septic tank for sewerage.How to get there: Ten minutes by boat from Roy Pier in Newport, Co Mayo, which is located beside the 16th-century Clare Island Castle, or Gráinne Uaile’s Castle as it’s known locally. Newport is about a 10-minute drive from Westport. Best feature: Unsurpassable views over Clew Bay and Croagh Patrick.Inis Saimer, Mall Quay, Ballyshannon, Co Donegal Inis Saimer, Mall Quay, Ballyshannon, Co DonegalO’Boyle Property, €299,000 AMVWhat’s on offer: A three-bed house on a private island with grounds of half an acre on the river Erne at Ballyshannon Harbour. The sheltered retreat is surrounded by natural flora and fauna. It is for sale by online auction unless sold in advance.Accommodation: The home extends to 219sq m (2,357sq ft) and would benefit from some modernisation; the agent notes it may qualify for the Vacant Property Refurbishment Grant. It features an open-plan kitchen/living space, a separate sittingroom and three bedrooms. It has a G Ber.How to get there: It has a private floating jetty, allowing the property to be accessed from the mainland. Best features: River views; close to amenities.Lake House, Cameron Island, Lough Derg, Co Tipperary Cameron Island grounds Lake House, Cameron Island, Lough Derg, Co TipperaryLisney Sotheby’s International Realty, €950,000What’s on offer: A fine three-bedroom lakefront home on 1.7 acres of Cameron Island on Lough Derg. It is the only home on the island, and the rest of the circa-100-acre island is native woodland.Accommodation: The three-bedroom home extends to 187sq m (2,008sq ft) and comprises a kitchen/dining/livingroom, a study, utility room, three bedrooms – one of which is en suite – and a bathroom. It is in good condition and has a C3 Ber.How to get there: Five minutes by boat from a quay on the mainland. It is a 15-minute drive from Nenagh in Co Tipperary and less than an hour from both Limerick city and Shannon Airport. Best feature: In addition to lake access, the grounds of the Lake House feature stunning gardens.Ardoileán (High Island), Claddaghduff, Co Galway Ardoileán monastic ruins Ardoileán (High Island), Claddaghduff, Co GalwaySpencer Auctioneers, €750,000What’s on offer: An 80-acre island about 3km off the coast of Connemara, close to Claddaghduff and Inishbofin. It is suitable for grazing and features two natural freshwater lakes. The island measures 1.2km by 0.4km and rises to a maximum height of 63.3m above sea level. It is a Special Protection Area under the EU Bird Directive of special conservation interest for the barnacle goose, fulmar and Arctic tern.Accommodation: There are stone ruins of a seventh-century monastic settlement on the island which have national monument status and are therefore in Government ownership. Close to the southern landing area, there is a more modern building measuring 7m by 14m of timber construction with a galvanised roof. There is a septic tank on site, which has potential for a building to be constructed subject to the necessary planning permission.How to get there: By private rib boat from Claddaghduff or by helicopter.Best feature: The island is a haven for birds.