The widow and daughter of an Australian property tycoon said yesterday that they were "perplexed" by reports linking their luxury yacht to the Madeleine McCann investigation.

The vessel, Willpower, was moored at Barcelona in Spain around the time when a woman with an Australian accent reportedly asked a British man if he was there to deliver her "new daughter".

The McCanns' private detectives last week launched an appeal for information about the mysterious woman, described as a Victoria Beckham lookalike.

Rhonda Wyllie and Melissa Karlson, the widow and daughter of the late Australian multi-millionaire Bill Wyllie, insisted they were not in Barcelona at that time.

A Wyllie Group spokesman said: "Rhonda and Melissa are perplexed by the media coverage of the past 24 hours, especially given that neither of them was actually in Spain on the night in question."

There is no suggestion that they or any of their yacht's crew had anything to do with Madeleine's disappearance.

The little girl was nearly four when she went missing from her family's holiday apartment in Praia da Luz in Portugal on 3 May 2007 while her parents dined with friends nearby.

Just over 72 hours later, in the early hours of 7 May, two British men saw the Victoria Beckham lookalike while on a night out in the popular Port Olimpic Marina in Barcelona.

When one of the British men approached and spoke to her, she reportedly asked him: "Are you here to deliver my new daughter?"

After speaking to the witness, the woman went into a bar next door, where she had a heated conversation with a local in what seemed to be fluent Spanish.

McCann family spokesman Clarence Mitchell said the private detectives were investigating boat movements around Portugal and Spain.

They are also going through information provided by the public in response to the appeal, including "dozens" of possible names of the woman seen in Barcelona.

Mr Mitchell said the investigators were ready to travel to Australia at short notice.

"If anything urgent happens and they need to go to Australia quickly, they will. But they're not on the verge of setting off," he said.

The new lead has given Madeleine's parents, Kate and Gerry McCann, "renewed hope", her grandmother said today.

Susan Healey, Mrs McCann's mother, told Hello! magazine: "Although we try to be hopeful, there are times when we think 'But it's been such a long time'.

"Sometimes it feels almost unbearable. Then there's a new lead or clue, or you hear about another child that went missing who's been found alive and it gives you a lift.

"News of missing children being found safe and well years later has helped Kate and Gerry remain positive too."