The daily said Dooley, 25, a cannabis farmer who was not invited to the royal wedding in Windsor, handed the four-inch blade to a bouncer outside the club in Kingston, southwest London.
London's Metropolitan Police did not name Dooley but confirmed they were called by security to the club "after a man openly declared he had a knife as he attempted to enter the club".
The incident happened just hours after Saturday's wedding of Prince Harry and Meghan.
"When officers arrived at 01.55 hrs enquiries led them to a hotel in Kingston and two men in their 20s were spoken to by officers in connection with the incident.
"One of the men also voluntarily surrendered a noxious spray. Both men, who were visitors to the UK, were warned about their actions," the statement said.
"Neither was arrested, no further action was taken and enquiries are complete," it added.
It is illegal to carry any knife in a public place in England except for folding pocket knives with blades measuring three inches (7.62 centimetres) or less.
Police commander Sally Benatar was quoted in the statement as saying: "The items were handed over voluntarily and there was no ongoing risk so the investigation was closed with warnings given".
The Sun quoted Dooley as telling someone outside the club: "I just brought it because Donald Trump said London was like a warzone. I had it for protection".
Dooley flew into London last week with his brother and mother, the ex-wife of Markle's half-brother Thomas, who was also not invited to the nuptials.
The run-up to the royal wedding was overshadowed by the media circus surrounding Markle's family.
Her father pulled out at the last minute after getting caught up in a paparazzi scandal and then undergoing a heart operation while her mother was the only family member to attend.
Trump has stirred controversy with repeated references to security issues in Britain.
In a speech at the National Rifle Association in Texas this month, he talked about knife crime in London, comparing a hospital in the city to a "war zone".
Knife-related crimes rose by 23 percent in London last year and a spate of stabbings and shootings have left more than 50 people dead this year.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)
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