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On the sign:
ON THIS SPOT A WELL WAS FIRST MADE. AND A HOUSE OF CORRECTION BUILT THEREON. BY HENRY WALLIS. MAYOR OF LONDON. IN THE YEAR 1282.
NATHANIEL WRIGHT ARCHITECT
[and on the other side] THE WELL WAS DISCOVERED. MUCH ENLARGED. AND THIS PUMP ERECTED. IN THE YEAR 1799. BY THE CONTRIBUTIONS OF THE BANK OF ENGLAND. THE EAST INDIA COMPANY THE NEIGHBOURING FIRE OFFICES. TOGETHER WITH THE BANKERS & TRADERS OF THE WARD OF CORNHILL.
The sign stands on an old water pump, which in the past (in the 13th century), had a well there, and a house of correction (a kind of prison for the poor). Over the years, the house of correction was destroyed and the well was forgotten. In 1799 the well was rediscovered, and then the water pump was installed.