Critics in the marginal south-west London constituency want him to resign to give the Tories time to groom another candidate before the next general election.
The challenge has been prompted by the colourful personal life and extra- parliamentary interests of the former Secretary of State for National Heritage.
Mr Mellor's future will be put to a vote at the Putney Conservative Association's annual meeting tomorrow night. About 100 people normally attend.
A motion put down by Garret Smyth, a film producer, and seconded by Noel Feldman, an airline pilot, thanks him for his services since 1979, and goes on: "Following his recent activities we call upon him to stand down in advance of the next election to allow time for Putney Conservative Association to select a candidate who can hold the seat at the next election."
Mr Mellor, 46, held the seat with a 7,526 majority at the last election. He quit as Secretary of State for National Heritage in 1992 following his affair with the actress, Antonia de Sancha, and his failure to declare a family holiday to Spain paid for by Mona Bauwens, daughter of a PLO official.
Now reputed to be topping up his £31,687 MP's salary with £250,000 a year from media appearances and business consultancies, Mr Mellor separated from his wife Judith last year to set up home with Lady Cobham. He said in a statement: "The proposers of the motion are well-known troublemakers in the association and I am confident of securing my association's backing."
The MP, recently named Radio Personality of the Year by the Variety Club, yesterday got the full support of his association chairwoman, Alex Elliott. She said the 24-strong executive council - which included one of those now seeking to drop him - gave the MP their full support on 24 January. "There is a small group who set out to cause trouble," she said. "As a constituency MP he is tremendously hard working. This is an attack on his personal life."Reuse content