The News of the World reports that Mr Richards, who is married and aged 48, has been having an affair with a 28-year-old divorcee, public-relations woman Julia Felthouse. He will be under strong pressure to quit under John Major's firm ruling that ministers caught up in scandal should go voluntarily.
Mr Richards, MP for Clwyd North West and a father of three, issued a statement through Conservative Central Office insisting: "I have nothing to say." A party spokeswoman declined to comment on "unsubstantiated allegations".
However, the newspaper published detailed allegations about the MP's reported relationship with Ms Felthouse, a former publicity officer for the National Canine Defence League.
Mr Richards, an ex-Royal Marine and television newsreader, is no stranger to the headlines. Soon after becoming a minister in July 1994, he accused Welsh Labour councillors of being "short, fat and fundamentally corrupt" and was forced to retract by the then Welsh Secretary, John Redwood. He also had to apologise for calling Peter Hain MP "a liar" in the Commons.Reuse content