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From the Wikipedia page [1]

Barnet Fair is an annual horse and pleasure fair held near Mays Lane Barnet on the first Monday in September. Barnet Horse Fair takes place over three days starting on the 4th September. It still operates under its royal Charter which is issued by Barnet council.

The fair began in 1588 when Queen Elizabeth I granted a charter to the Lord of the Manor of Barnet to hold a fair twice yearly, in addition to the weekly Barnet Market.[2] Originally held in June and October, Lord John Tomlinson changed the dates to April and September in 1758 for the reason of improving business.[2] From 1881, the April fair ceased.

The focus of the fair was its livestock, with animals being brought from across the United Kingdom. In 1834, The Times reported that Barnet Fair was England's largest cattle market, with up to 40,000 animals on display.

From the eighteenth century, the festivities also used to include horse racing, although these ceased in 1870 when the railway station was built on the ground in which they had been held.

The focus in the present-day Barnet Fair is no longer on horses and other livestock; but it is rather a pleasure fair instead.

The term 'Barnet Fair', normally shortened to 'Barnet', has become rhyming slang for 'hair'.

The London Borough of Barnet Council page is [2]