He told the inquiry that the home of Tinglan Hong - the mother of his daughter - was surrounded by paparazzi, one of whom went on to allegedly verbally abuse Tinglan's 63-year-old mother and "menace" her with his car.
Hugh said: "The house where the mother of my child and my child were besieged was surrounded by these paparazzi, and I asked my lawyer what could possibly be done. The lawyer said that if they could get pictures of the paparazzi it could increase the likelihood of them being 'called off'.
"The 63-year-old grandmother of the child went out into the street and took a picture of a man sitting in a car with a great big camera."
The photographer then allegedly "wound the window down and shouted a lot of abuse at her and then as she crossed the road he menaced her with his car".
"He drove at her very fast and made her jump out of the way, and at the end of the road he did a u-turn, came back and menaced her again with his car," said Hugh.
He claimed police are visiting Tinglan Hong to discuss the incident on Wednesday.
Tinglan Hong was last week granted an injunction to prevent her being "hounded" by photographers outside her home who had made her life "unbearable".
Hugh also alleged that the story of Tinglan Hong's pregnancy was originally being investigated by the News of the World, and that "one journalist in particular" who is now with the Daily Mail was working on it.
He said: "When the NOTW was closed down that journalist appears to have moved over to the Daily Mail, because a lot of this work and these calls came from that journalist now representing the Daily Mail."
He said the newspaper had "all the information" including the false name Tinglan Hong had used for her admittance to hospital. Hugh said he believes the details had been leaked by the hospital.
The story of his baby daughter's birth was eventually broken by an American publication, and Hugh claims the Daily Mail had only held off publishing first because: "They didn't want to print the story based solely on their hospital source because that might have been unethical or possibly illegal.
"So they needed a comment from my side and that is why I said nothing."
The Daily Mail refuted Hugh's claims, saying: "The Daily Mail unequivocally denies Hugh Grant's allegation that it secured information about the birth of his child from a source at the hospital.
"In fact the information came from a source in his show-business circle more than two weeks after the birth.
"We then spent a further two weeks seeking a response to the story from his publicists.
"None was forthcoming and indeed we did not publish anything until Grant's publicist issued a statement describing the baby as the product of a 'fleeting affair'.
"Throughout the Mail behaved with total journalistic propriety."
The inquiry continues.
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