The health secretary met with the British monarch at Buckingham Palace during a reception to thank those involved with the Diamond Jubilee celebrations earlier this year.
Hunt congratulated the royal over her appearance in an Olympics skit with Daniel Craig, reports The Daily Telegraph.
He told her: "I read about a Japanese tourist who said afterwards how wonderful our Queen must be to take part in that as they would never get their emperor to jump out of the plane."
Hunt was then apparently met with a "tumbleweed" moment from the Queen, before she smiled and moved on.
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The Duke of Edinburgh afterwards shook hands with the MP, asking him bluntly: "Who are you?"
After explaining he is currently the health secretary, having been the culture secretary at the time of the Diamond Jubilee, Prince Philip replied: "Well they do move you people on a lot."
Gary Barlow and celebrity chef Heston Blumenthal were also among the guests invited to Buckingham Palace.
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