"mark on the hull of a British ship showing how deeply she may be loaded," 1876 (Plimsoll's mark), from Samuel Plimsoll (1824-1898), M.P. for Derby and advocate of shipping reforms (which were embodied in the Merchant Shipping Act of 1876 and required the load-line mark).
The sense was extended by 1907 to rubber-soled canvas shoe (equivalent of American English sneakers) because the band around the shoes that holds the two parts together reminded people of a ship's Plimsoll line; this sense perhaps also was reinforced by sound association with sole (n.1), which sometimes influenced the spelling to plimsole. The surname is of Huguenot origin.