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By the end of the 18th century, it was apparent that the old London Bridge — by then over 600 years old — needed to be replaced. It was narrow and decrepit, and blocked river traffic. In 1799, a competition for designs to replace the old bridge was held. Entrants included Thomas Telford, whose proposal of a single iron arch spanning 600 feet (180 m) was rejected as unfeasible and impractical. John Rennie won the competition with a more conventional design of five stone arches. It was built 100 feet (30 m) west (upstream) of the original site by Jolliffe and Banks of Merstham, Surrey, under the supervision of Rennie's son. Work began in 1824 and the foundation stone was laid, in the southern coffer dam, on 15 June 1825.

The old bridge continued in use while the new bridge was being built, and was demolished after the latter opened in 1831. New approach roads had to be built, which cost three times as much as the bridge itself. The total costs, around £2.5 million (£186 million as of 2013), were shared by the British Government and the Corporation of London.

Rennie's bridge was 928 feet (283 m) long and 49 feet (15 m) wide, constructed from Haytor granite. The official opening took place on 1 August 1831; King William IV and Queen Adelaide attended a banquet in a pavilion erected on the bridge.

In 1896 the bridge was the busiest point in London, and one of its most congested; 8,000 pedestrians and 900 vehicles crossed every hour. It was widened by 13 feet, using granite corbels; but subsequent surveys showed that the bridge was sinking an inch (about 2.5 cm) every eight years; and by 1924, the east side had sunk some three to four inches (about 9 cm) lower than the west side. The bridge would have to be removed and replaced.