Artaxerxes
Look out, he's got a gnu!
I googled mudlarking and found this thread do you need permits to do it in the rest of the country? I don't think anyone would notice if I went and poked about the mud. There was tons of industry here so I think there might be some interesting stuff waiting to be found!
You need a licence to dig and there are parts you need to avoid due to being Scheduled Ancient Monuments.
But walking the foreshore and having a poke and search for something cool is quite fun. I was amazed how many animal bones there are down by Greenwich.