Steven Van Lonkhuyzen, 37, and sons Ethan, seven and Timothy, five, hit trouble when they took a wrong turning on the 1000-mile journey from their Brisbane home to Cairns. Their car got stuck in mud, leaving them stranded in the remote Expedition National Park with no mobile phone signal and only enough food and water for their scheduled four-day camping trip.

A massive search covered an area of Queensland three times the size of the UK, but hopes began to fade when the family was not found after more than a week of extreme weather including storms, flooding and scorching heat.

But Steven had carefully rationed the trio’s meagre supplies, and they managed to catch precious rainwater by putting out containers. But they were down to their last few slices of bread when they were eventually found in their car on Sunday by cattle farmer Tom Wagner, who had begun his own motorcycle search in response to police appeals for help.

“They were pretty hungry by the time I got to them, and pretty happy to see me,” Mr Wagner told The Independent: “Luckily it rained, otherwise they would have perished.”

Police officers and park rangers had to winch themselves across a road washed away by storms to reach the lucky family, who were found around 185 miles from where they had last been seen at a service station. They were taken to hospital in Taroom, and are expected to make a full recovery.

Acting Superintendent Mick Bianchi, who co-ordinated the police search, told The Guardian: “We were very concerned about their welfare. It was very hot and humid.”

He added: “I would like to thank Mr Wagner, who managed to find them off his own bat. It’s pretty indicative of the way country people pitch in and help each other.”