Not too sure about night clubs, certainly the music hall/Vaudeville theatre program was where most magicians performed from the late 19th right into the 1930s, where a constantly running program of performers (jugglers, singers, acrobats, comedians etc.) presented fifteen to twenty minute acts in a rotating order. Audiences walked in, watched a few acts and left rather than watch a single performer for a whole performance.
The big names with a big enough pull would either headline the Vaudeville or in rare cases do a whole show in the older style, but we're talking big names (Thurston, Kellar, Alexander, Chung Ling Soo etc.).
Worth reading anything by Jim Steinmeyer or Mike Caveney (though the latter's books are rarer than rocking horse poo) or perhaps buying the Taschen book Magic, 1400s to 1950s written by these two (absolutely beautiful book but I don't have this myself the price made my wallet cramp).
Other than that might be worth emailing the Magic Circle at
enquiries@TheMagicCircle.co.uk with your query.