Lobsters can be found regulary across the London clay divisons with the most common of these Hoploparia Gammaroides which can be found at most sites.
However the other species of lobsters tend to be much rarer such as Glyphea scabra [Trachysoma scabrum] which can only be found extremely rarely in a few sites such as seasalter.
Complete lobsters are also extremely rare in the London Clay as they are often brocken up into segments. When searching for lobster fossils both the foreshore and the beach should yield results as they are quite notable from their distict black apperance in a beige coloured nodule.