Green’s Dictionary of Slang

to deceive or persuade by glib talk.

1938		J. Curtis They Drive by Night 84: Try to fanny it out the way this bloke had said.
1956		J. Curtis Look Long Upon a Monkey 28: They were passing a screw, so Stringy kept quiet for a few paces before going on, still fannying they were discussing other blokes.
1961		T. Taylor Baron’s Court All Change (2011) 97: ‘To try and fanny someone that’s cuter than you are’.
1975		‘P.B. Yuill’ Hazell and the Three-card Trick (1977) 156: It was his own money, saved up from a lifetime of blagging and fannying suckers.
1989		J. Morton Lowspeak.
1998		G. Burn Happy Like Murderers 128: He’d talk to the girls and, in the words of somebody who knew him then, ‘fanny about’.