Are you planning traveling to the UK or doing research or something?
These replies will help.

I would say that in terms of land based casinos that blackjack and roulette are by far the most popular games that you'll find in the casinos there. I don't think that they have the room in the cities for the big slots casinos like there are in the US. I'm not sure about what games they really favor online but I think that in terms of offline land based casino games that blackjack and roulette is where it's at for them.

I think this guy was biased, and British, and thought too much of British folks, but still interesting:
"Yeah players from the UK generally like playing table games and games where they can somewhat control the outcome and or have more in way of betting decisions that they can make. I think that their favorite game is blackjack. If you go to the Hard Rock, Ritz Club or any other land based casino found throughout London and or the UK you'll generally find that we don't have too many slots games and in some cases any. I think that players from the United Kingdom in general are more savvy players and thus as a result have more drive to play games like I said where they can control the outcome of the game play a bit more. They're smarter and sharper players.

That's for land based casino gaming however online I would say that a lot of the women in the UK who love to play Bingo and trust me there's a ton of them also enjoy to indulge in playing video poker and slots games over and above the other games. I also think it's all about the player. A proper punter for example will want to bet on sports which has nothing to do with casino gambling whatsoever or perhaps indulge in playing in a higher stakes poker game."