Barnet has become a fairly commonly used bit of rhyming slang.
Barnet Fair = hair.
The first Barnet horse fair was in 1588, Queen Elizabeth decreed the North London town could have two fairs a year. It is now only held once a year, in September and is less of a commercial event and more of a pleasure event.
So let's use the word in a sentence:
"I can't remember when my missus' barnet was blonde", which translates to "My wife has never had blonde hair"