Living in London i often wondered what lurked in the Thames, you would see oddball lads fishing near the Thames Barrier when I lived in Charlton, but no traps in South-East; at least where I lived anyway. We did find a few lads a further down the stream who were trapping for crayfish, though.
Half-arsed research led us to the National Institute of Crayfish Trappers (NCIT), (Later featured in the Grauniad), and their ventures into trapping in waterways up and down the country.
Why crayfish, I hear you ask. In the 70s, the UK government introduced the American Signal crayfish to UK waterways, ostensibly to sell to the Norwegians, whose economy was booming at the time. If research had been carried out properly, they'd have found out the American Signal carried a crayfish plague, which wiped out most of the native population. American Signal had an inbuilt herd immunity.
Like most hairbrained government schemes of their ilk, it was quietly mothballed and after a day or two's desultory press, forgotten. Meanwhile, the American signal was causing havoc in the waterways and wiping out all kinds of species by shoving its knob about and causing an imbalance to native UK species. There is a DEFRA report, if you want to read it
The NCIT is mostly a labour of love from a lad called Crayfish Bob, but he's done well out of it I believe - the American Signal has a much more delicate taste than most of the chinese farm-produced stuff. You can get hold of some mitten crabs in the Thames too, though I'd be loate to eat much from some of the stretches of that water now.
Particularly round the Greenwich peninsula, there's a lot of TPH in the soil from the old refinery that would no doubt cause some problems, however slight.
The lobsters remain a more obscure challenge around London waterways and I dont really have the time or werewithal these days to look into it much. I did hear of a few lads trapping in West London years ago but i think there was only a smattering there
Perhaps for the southern trapper, heading towards the far coast is the answer. On a clear day you could see France in the distance, of course