These secret soirees are organised by the Common Sense Club, which takes its name from the book by the social reformer Tom Paine and has close links with Republic, the British republican movement.
It provides a forum to discuss "constitutional reform", a euphemism for abolishing the monarchy, the institution Paine compared to "something kept behind a curtain, about which there is a great deal of bustle and fuss, and an air of seeming solemnity...but when the curtain happens to open, and the company see what it is, they burst into laughter".
Its six founder members are Professor Stephen Haseler, chairman of Republic, Jon Temple, the group's secretary, Anthony Holden, twice biographer of the Prince of Wales, Brian Basham, a public relations consultant , Peter Singer, a former journalist, and Roy Greenslade, a former editor of the Daily Mirror. They have since elected a seventh member, John Norton, a banker who is married to the Labour MP Marjorie Mowlam.
"The key thing is that a lot of people feel quite strongly about this issue but don't like to talk in public about it," explained Professor Haseler. "The higher up people are, the less they feel they can say because of the establishment problem."
Of the club's monthly meetings, Mr Greenslade said: "They are convivial occasions in which we discuss the bringing down of the monarchy. It's good food at L'Etoile in Charlotte Street and six of us invite a guest each.
"They don't have to be republicans but they are always opinion-formers.
"We are there to rid us of the monarchy before we move into the 21st Century. People say: 'Come on, it's all a waste of time. You little six gathered in your little garret. Can you be serious?" But we've had MPs, businessmen and journalists, including the editor of the Economist and two editors of national newspapers."