The TV presenter described her encounter with the royal, who died on Friday (9 April) at home with his family, while presenting the ITV talk show on Monday morning (12 April).
The pair met at an event for the Duke of Edinburgh award, with Reid describing the Queen’s husband as being “incredibly direct”.
“I met him once,” she recalled. “He notoriously did not like small talk and yet he had to do how many solo engagements - 22,000? And 5,000 speeches. He was involved with 800 charities. He just did so much, and so obviously he had to do small talk with millions of people.”
Reid continued: “It was at a Duke of Edinburgh gold award ceremony, and he said to me in the line-up, ‘Well, did you do one of these?’
“And I said, ‘I did, but I failed to finish.’ And he said, ‘Ugh, what on earth was wrong with you?’ and then moved on to the next person.”
The panel, including Reid, then broke out in laughter, with the presenter continuing: “The thing is though, he said it in that sort of withering way, but at the same time, you knew it was made with a mischievous glint in his eye. It made you question your whole life.”
Following his death, Prince Philip was honoured at Sunday night’s Bafta film ceremony.
His funeral will take place on Saturday (19 April).