The coin sold is known as a "Pattern" version, as it was presented as a prototype, but never went in to production.
It is the first time that any of the Pattern coins have come up for auction.
Commenting on the record price, a spokesperson for the auction house, AH Baldwin and Sons said: "No other bronze coin has ever come close."
"I think the last was in the region of 15,000 pounds," he was quoted as saying by the BBC.
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The eventual price achieved was nearly double initial estimates.
A further seven pennies, known as currency coins, were produced in 1933 for ceremonial purposes, but none have recently come on sale.
It is thought the currency coins could be worth twice as much as the Pattern versions.
The reason so few were produced was that the Royal Mint had a surplus of penny coins in 1932, and did not need any more in the following year.
Others, it is thought, have been buried under buildings as part of a "time capsule".