Green’s Dictionary of Slang

Queen Anne’s fan n.

In phrases

make Queen Ann’s fan (v.)

to thumb one’s nose.

1923		J. Manchon Le Slang.
1940		M. Marples Public School Slang 163: To cock (1702) or more usually today to pull a snook ( =nose), to make a gesture of derision by applying the thumb to the nose and extending the fingers [...] known also ( [...] as taking a sight, working the coffee-mill, taking a grinder, pulling bacon, making a long nose and making Queen Anne’s fan.