Engineering Timelines describes the harrowing rapids under Old London Bridge, which stood in various forms from the 12th through the 18th centuries:
A major feature of [Old London] bridge was the effect it had on the Thames. The location of the bridge's 19 timber pier supports (starlings) was determined by riverbed conditions and this meant that they were varied in spacing across the river. Consequently, the arch spans varied in size too and boats navigating the arches encountered different currents and river conditions at each one. Some were more dangerous than others. Over the years, boatmen christened the arches with various names, such as Gut Lock and Long Entry.At the southern end of the bridge was a span without an arch and here a drawbridge was installed. At this point a toll was gathered from people wanting to cross the bridge. Many merchants opted to avoid the toll by moving cargo up and down the river in small boats.Navigating through the bridge in a boat could be very dangerous because the closeness and number of starlings backed up the river water, creating rapids. In some places the drop in water height from one side of the bridge to the other was more than the height of a man. Many people lost their lives 'shooting' the bridge and "Drowned at the bridge" became a common entry in the registers at nearby graveyards.Some Londoners presumably did as Cardinal Wolsey did. On his frequent visits to Greenwich to see Henry VIII, he would have his barge stopped above the bridge and get out and travel to Billingsgate by mule, where he would rejoin his barge — providing it had successfully negotiated the rapids.
One of the ladies of Queen Henrietta Maria (1609-1669), a woman named Anne Kirk, was drowned when a royal barge overturned while "shooting" the bridge.
The illustration is a detail from an artistic reconstruction of Old London Bridge based on an engraving from approximately 1600 by John Norden. From Old London Reconstructed. By the way, the bridge was entirely built up -- there were houses, businesses, even a chapel, perched on the bridge clear across the Thames.