Sydney Harbour is one of the great travel icons – its Opera House and the Harbour Bridge form an enduring shorthand for a fine city. All the more surprising, then, that the harbour’s islands are overlooked by most visitors.

There are six of them, each open to the public – and all but one (Cockatoo Island) is protected as part of Sydney Harbour National Park. they provide a startling new perspective on a familiar city and, at this time of year, they offer a welcome relief to the summer heat and crowds – though they could be busy next Thursday, when Australia Day is celebrated in the city.

Fort Denison and Goat Island heritage tours are run by the Sydney Harbour National Park, and cost A$27 (£18) and A$24 (£16) respectively, including the return ferry fare from Circular Quay. Book in advance (00 61 2 9274 5033; nationalparks.nsw.gov.au) or just turn up at the office in Cadman’s Cottage on George Street in the Rocks.

Captain Cook Cruises (00 61 2 9206 1100; captaincook. com.au) offers a range of trips, and also has a Harbour Explorer deal that takes you to three of the islands (Shark, Goat and Fort Denison) with a combination ticket that costs A$49 (£33). But I set about exploring them all.

Fort Denison

At only 70 metres long, this is the smallest of the islands and the closest to Sydney’s Central Business District. Daily at 1pm, the Fort Denison gun is fired and resounds around the harbour.

Back in the days of the penal colony, it was known as Pinchgut – and both held, and hanged, prisoners. its fortifications surround a jutting Martello Tower, built in 1856 complete with cannon to deter attack. none ever came.

Today, you can tour the tower; our lively guide provided a flavour of harbour life across two centuries.

Goat Island

Lying between Balmain and McMahons Point, this island got its name apparently because when viewed on the map it resembles a goat.

Once part of the inner ring of naval defences, Goat Island later became a whaling station and convict preserve. as you walk around its rim, you hear noises from the small operational shipyard. Today Goat Island smells of industry, not of history.

Nonetheless, the self-guided audio tour or the guided tours provided by the National Park’s rangers emphasise Goat Island’s convict past, pointing out the sentry wall, the police station, and the powder magazine. a path round the rim will take you to "Bony" Anderson’s chair – a narrow ledge carved in the rock face where Anderson, a convict was chained for two years for having dared to escape from the island.

Shark Island

The island lies almost beyond the confines of the harbour, adrift in Rose Bay, overlooking the purlieu of leafy Vaucluse on the southern shore, within sight of the heads that mark the exit to the ocean.the Aboriginal Guringai people once fished here, a pastime still popular with visitors. the landing fee (A$7/ £4.50) covers fishing rights for the day; it is included in the A$20 (£14) return fare on Captain Cook Cruises from Jetty 6, Circular Quay, or pier 26 at Darling Harbour.

The terrain is gentle, with palms and enormous hoop pines. the calm atmosphere is shattered on Boxing Day, when the gun goes off for the Sydney to Hobart yacht race.

Cockatoo island

Ten minutes on the Sydney Ferry from Circular Quay, and two kilometres west of the Harbour Bridge, "carry on camping" is the buzz phrase here. You can bring your own tent or hire one of the spacious, pre-erected RV-3 Oztents for a sleepover (from A$80/£56). Heritage homes, refurbished, are also for hire. You can also take the self-guided audio tour (A$5/£3.50 from the island’s office). it provides comprehensive coverage of the island’s past.

Aboriginals and convicts once haunted these precincts. the lower island is where a shipbuilding industry thrived, while up on the plateau sits the prison (excavation is still in progress). a guide-led tour each Sunday morning leads you through both, from isolation cells to the tunnels used as shelters during the second World War.

Rodd Island

Further west in Iron Cove, Rodd Island lies close to suburban Drumoyne on the eastern shore. Familiar to the shell gatherers of the Wangal tribe who used it as a campsite, the island was leased in 1842 by Brent Ross, a merchant-solicitor. When the actress Sarah Bernhardt toured Sydney in 1891, her dog was quarantined here.

The island rises gently from the boulders that form its shoreline, over lawns and past clusters of fig trees and serried Canary Island palms, to a caretaker’s house and a large colonial hall – which even has a dance floor.

Louis Pasteur based a research team here in 1889, seeking a virus to wipe out the rabbits then plaguing the city. Today, the island seems entirely rabbit free. it is popular as a Christmas party venue and haven for picnickers. There are tables, toilets, a jetty, and gentle views of the wealthy suburbs.

To reach it, hire a water taxi from a convenient wharf or jetty through Yellow Water Taxis (00 61 2 9299 0199; yellowwatertaxis.com.au).

Clark Island

The final isle lies off Darling Point on the harbour’s south shore. it was here, in 1789, that Lieutenant Ralph Clark arrived with prisoners aboard the first Fleet. his mission was to grow vegetables but the produce was soon pilfered and Clark gave up, leaving only his name.

Now visitors come to the island as part of an Aboriginal cultural cruise aboard the Tribal Warrior. the trip is operated by Captain Cook Cruises and leaves Circular Quay, Jetty 6, at 1pm daily.

Once on the island, visitors follow hidden paths among the bush, and then are shown fish traps placed in crevices of rock. the Aboriginal crew, wearing only loincloths and body paint, explain sacred tribal rituals, pointing out ceremonial locations, and they bring the tour to a close with the obligatory playing of a didgeridoo.

From the island’s highest rocks you appreciate the magnificence of the harbour with panoramic views that take in the Opera House, distant Manly, and Taronga Zoo.

Travel essentials: Sydney

Getting there

* the writer travelled with Qantas (08457 747 767; qantas.co.uk), which flies daily from Heathrow to Sydney. BA and Virgin Atlantic also fly direct.

* Many airlines offer a one-stop service with connections in the Gulf or South-east Asia, including Emirates and Singapore Airlines.

Staying there

* Harbourside Serviced Apartments (00 61 2 9963 4300; harboursideapartments.com.au) has apartments at McMahon’s Point from A$225 (£150) nightly.

More information

* Tourism Australia: australia.com

Reach across the water: Sydney Harbour’s islands provide a great escape from the crowds