Last year we spent the Millennium in Paris and the following week in London where we have an apartment. It's always amazing to me that so many American anglers visit England without fishing when there's so much good fishing within a couple of hours of London. Best of all, you can book a guided day and learn some of the wonderfully effective British bait techniques for coarse fish like trench or zander(walleye type), or cast flies or lures for trout, pike, sea bass and other saltwater species.
You will need a license. Coarse fish and non-migratory trout licenses only run about $4 - you may pay an additional fee for access to specific waters. Game fish in rivers run about $9 a day. You can fish just about anywhere for a price. I'd suggest that you contact a guide to start.
You probably won't need a boat. Most angling is done from the bank save for British trout reservoirs where you'll find boat, life jacket and gear packages.
You will need specialized gear if you fish on your own. Given live bait - maggots et al - is standard most towns have tackle shops that can suggest tackle and sell day tickets to fish local waters. Most of the local fishing is for coarse species and catch and release. Very light line - 2- to 4-pound test, size 18 or small snelled hooks a disgorger and some split shot and the wonderfully effective British floats work well.
This gear will also suit stillwater trout the budget options for bait, lure or fly fishing. Day ticket fishing on lakes and ponds isn't too expensive. Do realize that rainbow trout are about the only sp species most British anglers keep. If you want to fish some of the traditional British chalk streams prepare to pay $100 to $300 or more. Salmon fishing in Scotland may run a Daddy Warbucks $1600 a day, but you do get a guide to net the fish.
It's my considered opinion that the most interesting British angling is either coarse fishing for carp and lure or bait fishing for pike. Realize that carp in catch and release waters are extremely wary and seem best approached with the help of a guide who can show you some of the uniquely effective British floater and other systems. Pike fishing deserves attention too. When I wrote my book, STORIES BEHIND RECORD FISH, I discovered that 99 of the top 100 pike caught world wide were taken in Europe. If you plan to try pike fishing you might tough your usual bass gear and add a short wire trace plus some sort of unhooking gear and/or landing net. Bring some pike/bass plugs from home at British plugs, and all British gear seem extremely expensive when compared to US prices.
British landing nets, like British bait fishing floats, are definitely worth bringing home. They come with longer handles, mesh without knots and extensions that let you reach out over shore vegetation and rocks to net fish "green" so their survival chances on release are improved.