Flanders and Swann's first proper two-man show opened on New Years Eve 1956 at the New Lindsay Club, London.
At the Drop of a Hat went on to tour widely. Here is the route of the hat:
31-12-1956: New Lindsay Club, London
1956-1958: Fortune Theatre, London
August 1959: Edinburgh Festival, Scotland
1959-1960: Nine O'Clock Theatre, New York
1960-1961: American Tour:
Princeton
Wilmington
Pittsburgh
Cincinnati
Des Moines
Denver
Los Angeles
San Francisco
St Paul
St Louis
Chicago
Detroit
Toronto, Canada
Spring 1961: Geneva, Switzerland
Vevey
Lausanne
1962: UK tour:
Canterbury
Oxford
Leeds
Newcastle-upon-Tyne
Aberdeen
Edinburgh
Liverpool
Manchester
Birmingham
Toronto, Canada
1963: UK tour:
Richmond
Brighton
Cambridge
Coventry
Dublin, Eire
Oxford
Cambridge
Coventry
Bristol
At the Drop of a Hat then turned into At the Drop of Another Hat.
A scan of 'Playbill' magazine with Flanders and Swann on the front - also signed by them both.
Many thanks to Philip Hind for this scan.