He went on to tell viewers the team pretended to be key workers to book a boardroom at the Grosvenor House for the ceremony.
“I signed in as a bin man and no one questioned it,” he added.
The presenter continued to poke fun at Chancellor Rishi Sunak and Gordon Ramsay.
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“Let’s face it, the television industry has kept us all going during lockdown, that’s why tonight, unlike Rishi Sunak, I will be giving everyone universal credit.
“Everyone except Gordon Ramsay’s bank balance, which may still have a bit of work to do.”
In a further swipe at Meghan and Harry, the chat show host continued: “TV has actually brought families back together, well apart from one glaring exception when TV has had the opposite effect.”
During their chat, Meghan and Harry discussed their life in the Royal Family from their point of view.
At first, the Duchess of Sussex was interviewed alone before she was joined by her spouse.
The former Suits actress said she felt suicidal during her time in the family and, at one point, feared to be left alone.
She added she approached members of staff for help, but claimed she was told she couldn’t receive any.
Meghan and Harry also said an unnamed family member expressed concerns about the colour of their son Archie’s skin.
It’s not the first time the couple have been at the centre of a joke this month.
Grammy Awards 2021 host comedian Trevor Noah began this year’s ceremony telling viewers the event was socially-distanced due to the ongoing coronavirus pandemic.
He then pointed to the masked nominees, who were seated apart, and said there is “more tension in that tent than at a family reunion at Buckingham Palace”.
His joke came exactly a week after the Duke and Duchess of Sussex’s interview with Oprah aired in the US.