Depends what you mean by game fishers. Back in the twenties I believe that tuna appeared somewhere off the east coast of England and sparked a fashion for well heeled anglers to take them with a rod and line. The tuna apparently went away and so did the fishermen. I know that no game fisherman worth his salt would ever take fish with anything but a rod and line.
I just read that, Baggs - replied to your OP on the hoof as it were. Bluefin tuna are a protected species in British waters. If they are caught, they have to be returned to the sea. They cannot be “boated”. They are mostly caught by sea anglers (who are not, by definition, game anglers) fishing around wrecks for edible fish - there is no “trawling” involved so they are unlikely to be caught in large numbers, but as they can grow to quite enormous sizes, the temptation to go looking for a ‘specimen ’ will probably bring on a bit of a gold rush. Game anglers need a licence to fish for trout or grayling, and a special licence for species such as salmon or for sea trout. Sea anglers do not need a licence to fish for anything.