Hi Jojonas.
If you want old cameras, there's lots of choice in London but you will pay a price. Frankly, whatever you want in London - you will pay a price as it's the nation's capital and you will have to try very hard to find a bargain. If you want a good book, then try the bookshops on Charing Cross Road that runs from Oxford Street (opposite Centre Point tower) to Trafalgar Square. Not cheap but lots of good stuff.
If you want cameras, then Camera City near the British Museum in Bloomsbury might be worth a visit. York Cameras (nearby) is very expensive (in my opinion) and Aperture is great if you know what you want. They specialise in Nikon MF / AF both film and digital, Canon Digital (not film), Hasselblad, Leica, Contax and Rolleiflex. I've bough a fair bit from them and they are excellent to deal with.
Just around the corner is Jacobs Digital. They have a second-hand section and often have some quite unusual stuff. If you want to pay top dollar for plastic, then there's a Lomography store on the corner of Spitalfields Market. Uber-trendy and not my kind of place - but that's just me.
If I had a choice, there's a place called "The Real Camera Company" (RCC)on Dale Street in Manchester. Not only is Manchester a truly wonderful city (it's close to where I was born and spent my formative years) but there's a couple of good camera shops. The "London Camera Exchange" on Piccadilly Gardens in Manchester also has some interesting stuff and is quite cheap. The RCC has EVERYTHING. Loads of really old stuff, bodies, lenses, accessories and tons of books, old bags, tripods, projectors. I could spend days in there.
Brighton? I've spent a bit of time down there, mostly on business. There's some nice shops (I'll defer to Miles' greater knowledge).
If you want film, then check out Silverprint (near Waterloo in London), Ag Photographic (in Birmingham) and Morco (Mansfield, Nottinghamshire). They all sell in bulk and are as good as anywhere for a wide range of films / formats.
Hope you get what you're looking for.
Take care. Paul.