Many thanks to ChrisP of Ornamental Passions - and Rowing for Pleasure - for identifying the boat in Tull's terracotta sign as a peterboat.
Peterboats were used for fishing on the Thames from mediaeval times until the nineteenth century. Legend has it that they used to ferry passengers between the cathedrals of Saxon London; their use for fishing is better documented and endured for centuries. They were double-ended rowing boats, well-balanced, typically with a well in the middle to hold the catch.
The small peterboat died out in the mid-nineteenth century, having evolved into the larger 'bawley' which could be around 30 feet long with sails. They were particularly popular around Leigh, where they were used for shrimp fishing. Meanwhile, growing pollution was driving fishing boats out of London altogether: by the end of the century, the Greenwich whitebait fisheries which had used these boats disappeared. (Ironically, for some time before that, the pollution in the water actually seemed to benefit the fish!) One of the city's characteristic craft thus vanished from its river.