The actor, who has recently become a dad, continues to play a big part in the eight-year-old's life.
And he had a fun outing in store for Elizabeth's son this week – taking him to the cinema to see animated adventure The Pirates!.
The swashbuckling fun was sure to bring back fond memories for the pair. When Damian was four, Hugh gave him a pirate costume for Christmas.
The gift was his "favourite present", said Elizabeth, who added that the little boy – her son from a relationship with Steve Bing – wore it "every weekend".
"Uncle Hugh", as he is called by both Elizabeth and Damian, lives around the corner from the pair's London home. "We see an awful lot of him," says Elizabeth.
"Hugh adores him and it works very well indeed."
The Bridget Jones star must have been delighted to take Damian to see the film, in which he voices the part of the Pirate Captain.
Until now, young Damian, who was as dashing as his godfather in cream trousers and a suit jacket and tie, has been banned from watching Hugh's films.
"We're always trying to find something that Uncle Hugh has done that he can see, but they're full of swear words," says 46-year-old Elizabeth.
"We can't find any! He can't watch Four Weddings And A Funeral. He can't watch About A Boy. It's quite difficult trying to find stuff for kids."
Damian's other godfathers include Sir Elton John and his partner David Furnish.
Elizabeth says: "Damian's very lucky, actually, because he's got a lot of godfathers, and they all spoil him rotten."
Now he has a new father figure in his life in the form of Elizabeth's fiancé, cricketer Shane Warne.