There are numerous sites in which the London Clay division are exposed. The majority of these sites are within the north Kent coastline and Essex.
To my knowledge, the sites which are publicly accessible are all regestered Sites of Special Scientific Interest (SSSI) and therefor I recomend checking the legality of collecting at these sites.
https://naturalengland-defra.opendata.arcgis.com/datasets/Defra::sites-of-special-scientific-interest-england/about - Link to the SSSI Website
Details of some of these sites are below, with information about how to find fossils there and other bits of information.
Benton, M.J., Cook, E. and Hooker, J.J. 2005. Mesozoic and Tertiary Fossil Mammals and Birds of Great Britain. Geological Conservation Review Series No. 32, JNCC, Peterborough.
There are many other active London Clay sites such as Walton-on-the-naze, Steeple Bay, Burnham-on-Crouch, Upnor, Herne Bay and Studd Hill.
There are also many inactive London Clay sites which collection is not possible such as the Aveley pits in Essex which are now infilled.