Prime Minister Tony Abbott has told the Duke of Cambridge about the great spirit of the Rural Fire Service and mentioned his own work with the volunteer brigade in a meeting at Admiralty House in Sydney.

The prime minister on Thursday met the visiting Duke of Cambridge in the drawing room of Admiralty House, the harbourside official residence of the Governor-General, after Prince William had visited Winmalee in the Blue Mountains in the morning.

Winmalee was the scene of terrible devastation by bushfires last October and the duke remarked to Mr Abbott how stoic the survivors who’d told him their stories had been.

Mr Abbott asked William if he had enjoyed his visit to the Blue Mountains.

“A very good day, thank you. There were some incredible stories,” the prince said.

Prince William peers over the cliff edge at Narrow Neck Lookout near Katoomba. Picture: AAP

William recounted being told by one resident of his efforts to defend his own house before helping save his neighbour’s property.

Mr Abbott, a member of the Davidson RFS branch, told the prince: “I’m a member of the local volunteer Rural Fire Service,” before discussing the ferocity of the fires that burned for a fortnight and the spirit of volunteer firefighters.

“These guys will respond to the needs even if they’ve got to neglect their own properties. It’s a great embodiment of the volunteer spirit, a great example of mates looking after mates.”

Mr Abbott also told the prince that locals were worried that tourists and visitors thought the Blue Mountains was still devastated by fire.

“But it’s amazing how quickly the bush recovers and there’s still businesses, attractions,” Mr Abbott said.

The prince mentioned his visit to the Three Sisters.

“It was a beautiful area,” he said.

Kate and Prince George did not accompany the duke on his meeting with Mr Abbott.