You're right. Thames estuary has loads of chalk. Part of the chalk basin that forms the south coast chalk, brought up to the surface by faulting around Lewisham and Purfleet.
There's a reference to east coast colliers and chalk
here - says they could sell it for lime making? Anyway, ballast was dumped near the home port harbour mouth.
I'm sure I've seen it in the estuary on the North Side? You seen any there?