But at the high court today Grant was offered a full apology by the group, which also said it would pay his legal fees.
Grant has already said the damages will go to charity.
The 45-year-old and Khan said themselves that their February split after a three-year relationship was "amicable".
"The truth is that all the allegations and assertions are false," said solicitor Simon Smith representing Grant at the London court.
A statement from the About a Boy actor said: "I took this action because I was tired of the Daily Mail and Mail on Sunday publishing almost entirely fictional articles about my private life for their own financial gain.
"I'm also hoping that this statement in court might remind people that the so-called 'close friends' or 'close sources' on which these stories claim to be based almost never exist."
Grant was arrested in London earlier this week on suspicion of assaulting a photographer.
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