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1.
It's a classier version of bite me in that it's literal meaning is "Go away, asshole" but it is usually said to someone you like in a joking manner.

According to Fowlers, Princess Anne said it to a bunch of reporters sometime in the 1980's.

It's really obscure. Princess Anne and I are the only ones I know who say it.
"So, I was reading the comics this morning and noticed that Cathy is dieting for her wedding just like you are!"

"Oh, naff off..."
by ChaliceChick November 30, 2004
 
2.
a kinder way of telling someone to "fuck off", was first used in the book "Kes", but popularised in the british tv series "porridge", a comedy series about a prison and its occupants. Norman Stanley Fletcher used it constantly as a way of getting around tv censorship.
got any snouts fletch?,,, Naff off your erk no I aint!
by kulucriss January 05, 2008
 
3.
like saying piss off but in a more joking and friendly term. Usually used when someone is making a rude (but joking) remark about you.
'ooo you look grumpy'

'naff off'
by ewgvwg March 25, 2006