Some of the strictest on the planet. Honestly they're so convoluted that even our Police don't understand them! As it's shotguns in question I'll try to outline a few of the laws...
1: You need to hold a shotgun licence (maximum capacity of three shots) or a firearms licence (unlimited).
2: Minimum barrel length is 24".
3: Minimum overall gun length (including the stock at it's shortest setting) is 40".
4: Full auto is banned.
5: On a shotgun licence, cartridges must contain a minimum of 6 pieces of shot, which I think is 00 Buck. SOlid slug can only be used on a firearms licence, and only on home office cleared ranges (of which there are only 5 in the UK).
There are more, lots more, but I don't want to hijack someone's deviation to list them all. Google might be your friend if you want to know more.