The Hamiltons say Nadine Milroy-Sloan is glorifying in the sex allegations she has made against them.
Speaking this morning, Christine Hamilton said she would be willing to go through the trauma of another libel case to claim damages if the claims are proved untrue.
Neil Hamilton said: "This woman is still persisting in making these allegations to the police and glorifying in them."
Police are continuing their inquiry into allegations that the Hamiltons sexually assaulted the college lecturer. Ms Milroy-Sloan spent six hours being interviewed again at Barkingside police station in east London yesterday before celebrating her birthday with her parents and children.
Officers said they are continuing to investigate her allegations that the former Conservative minister and his wife sexually degraded her while another man raped her.
Speculation had been mounting that the police inquiries would be shelved after a call, alleged to exonerate the couple, was traced to Mrs Hamilton's mobile phone. The attack was said to have taken place in a flat in Ilford on May 5 at around 5pm - but the phone call placed Mrs Hamilton's mobile 13 miles away at around 5.40pm.