London Stone is the name given to a number of boundary stones which stand beside the rivers Thames and Medway, which formerly marked the limits of jurisdiction of the City of London.
In medieval times before the canalisation of the Thames, Staines-upon-Thames was the highest point at which the high tide was perceivable for a few minutes every semi-diurnal tide (twice a day), adding some millimetres to the water depth compared to more upstream parishes.
This London Stone marked the upstream limit of the City's rights. The official role of a London Corporation stone of 1285 beside Staines Bridge was set out with a grant of associated privileges in a charter of Edward I. Its use by the river is confirmed by the semi-circular indentations (on the right hand face in the photo), to cater to tow ropes of horse-drawn boats rubbing against the stone.
More at Wikipedia
https://en.wikipedia.org/wiki/London_Stone_%28riparian%29
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