1950s: euphemism for fuck; compare with eff.

• The first recorded example of naff, meaning ‘lacking taste or style’, is from the script of the BBC radio programme Round the Horne by Barry Took and Marty Feldman (1966): ‘I couldn't be doing with a garden like this. I mean all them horrible little naff gnomes.’ One of the most popular theories about its origin is the suggestion that the word was formed from the initial letters of Normal As F— or Not Available For F—ing, but more likely is the idea that it is from Polari (a form of theatrical slang incorporating Italian words, rhyming slang, and Romany, used especially by gay people), and that it comes ultimately from Italian gnaffa ‘despicable person’. Naff off, meaning ‘go away!’, is probably a different word, which may be a variant of eff, as in ‘eff off!’ Its first recorded use is from Keith Waterhouse's novel Billy Liar (1959): ‘Naff off, Stamp, for Christ sake!’ It was often used in the script of the BBC comedy series Porridge as an acceptable substitute for the bad language characteristically used in prison, and in 1982 Princess Anne was famously supposed to have told reporters to ‘Naff off!’ when they photographed her after she had fallen from her horse.

1960s: perhaps from Polari.