Partridge, A Dictionary of Slang and Unconventional English, 8th ed.:Barnet Fair.
The hair: rhyming s., orig. (-1857) thieves'. 'Ducange Anglicus'. In C. 20, often Barnet
Green, The Cassell Dictionary of Slang:barnet n.
[mid-19C+] hair. [rhy. sl. Barnet Fair
= hair]barnet fair n.
[mid-19C+] the hair [...] [rhy. sl.: the actual Barnet Fair fl.
16C-18C as the country's major horse fair; [...]
Ayto / Simpson, The Oxford Dictionary of Modern Slangbarnet noun Brit. 1
The hair. 1931-. F. Norman
They send you to a doss house, so that you can get lice in your barnet (1962) [...] [Short for Barnet fair
, rhyming slang for 'hair', from the name of the London borough of Barnet
barnet Noun. Hair. From the Cockney rhyming slang barnet fair. [Mid 1800s]http://www.probertencyclopaedia.com/Z_BARNET.HTM
Barnet (from Barnet fair) is London Cockney rhyming slang for hair.