Green’s Dictionary of Slang

fill n.

In phrases

give someone a fill(-up) (v.)

(UK Und.) to deceive.

1882		‘The Jargon of Thieves’ in Derry Jrnl 8 Sept. 6/6: If a hoodlum should remark , ‘I gave the bluebelly a fill,’ he would [...] mean that he had succeeded in deceiving a police officer.
1902		Reno Gaz.-Jrnl (NV) 13 Mar. 1/5: [headline] An Intelligent Man ‘Steamboated’ by a Soldier boy who Gave him a Great ‘Fill up’.
1909		J. Ware Passing Eng. of the Victorian Era 130/2: Fill, To give a (Thieves’). To deceive, e.g., ‘I gave the blue belly a fill’ – would mean that you sent the policeman on a wrong scent.