Hi DBH,
It's been a few years since I went to a casino, yes that's right I'm a good bit over 18 
I'm not entirely sure about the cash games stakes, but they tend to run tournaments starting around £25 entry.
There are lots of casinos in and around Brighton/Hove, but I would personally stick to the main branded ones. I understand the most popular are The Rendezvous and Grosvenor.
I don't have any personal experience of these so it's probably best to do an internet search, locate their websites and find out the opening times/dress code etc.
Just be responsible with your BR, it is extremely easy to get carried away with both money and time in casino due to the many distractions. I would of course also recommend (from personal experience) staying away from games such as roulette etc as these are heavily weighted in favour of the house (or just allocate a couple of quid to donk around with/fun purposes).
I always used to go down with friends (more fun for less money) and always set myself a monetry limit (stop-loss).
Best of luck,
Bart