In classic literature (such as Pride and Prejudice) Barnet refers to the city High Barnet within the borough rather than the borough itself which was not formed until 1965.
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“Somewhere near Barnet, north of London,” said Frank, giving him the paper.
Daphne du Maurier. Rebecca (1938)
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After making every possible inquiry on that side London, Colonel F. came on into Hertfordshire, anxiously renewing them at all the turnpikes, and at the inns in Barnet and Hatfield, but without any success—no such people had been seen to pass through.