In order to play in the UK at online casinos they must be licensed. Some online casinos decided not to opt in for a license do to the fees they must pay to the United Kingdom government. There is a decent amount of online casinos that have decided to work with the government and have legal casinos. What this means for the UK citizens is they must only pick to play at online casinos which accept them as users.
It might be a bit disappointing when you see a casino that you might find appealing including their bonus offer only to be turned down. One fact is that one of the groups that does allow UK players owns more than thirty different casinos. This group may aggressively get you to change casinos by offering you high bonus deals for switching.
This is not recommended as the casino you sign up may be the one that pays out the most. I always recommend to play at just one casino for long term if you want to hit the largest jackpots. Not always does it happen the first month but it will happen at some point the longer you play at a single casino site.