Williams told Scott Mills and Chris Stark on their final BBC Radio Five Live morning show — reported via The Sun — that he met the 80-year-old musical legend in Tahiti, but didn't immediately recognise the Oscar-winning star.
He said: "It was like ‘hi I’m John’ and ‘hi I'm Rob’ and ‘hi I’m Steve’ and ‘Hi, I’m Barbra’. ‘Hello Barbra, I’m pleased to meet you’.
"Nice old lady. Then I sat down next to Barbra. And it was Barbra Streisand. And I was like: ‘Oh, ahh’.”
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Any showbiz ego on Williams' part, however, was soon ditched when Streisand was equally clueless about him.
There was confusion about the star's identity when the group began talking about the charity sport initiative Soccer Aid, which Williams started with pal Jonathan Wilkes in 2006.
Williams said: “It turns out that she actually thought I was a football player. People were talking about Soccer Aid, and she just presumed I played football.
"And then I was like ‘oh, no, no, no, I’m a singer’. And she was like: ‘That’s nice’.”
During the interview, Williams also revealed that his first ever holiday away from his parents was as a 17-year-old with Take That bandmate Mark Owen in Tenerife when the group was "just on the precipice of international stardom".
"We were given £500 by our then manager to go away on holiday. That £500 got us a week away and our spending money," he said.
Williams added: "I had to share a room with Mark Owen and then, on the final couple of nights, we ended up working in a bar.
"We thought it would be a laugh. We actually didn't get paid. We just did it because we fancied doing it and it would be fun."
Mills noted that Williams has a history of making up outlandish anecdotes in order to make interviews more interesting, but the star assured him it was a "true story".
He said: "Ask Mark Owen. Like Joni Mitchell, Mark Owen never lies."
The star appeared on the show to promote his upcoming album XXV, which celebrates a quarter of a century of his solo career.
The album features reimagined versions of some of his greatest hits, reinvented and revamped with the aid of an orchestra.
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