I'm having the same problem. I haven't tried Opera, but I would prefer not to use Opera.
I use Linux (the latest release of CrunchBang, which is based on Debian), and Iceweasel (basically Firefox). I also have Chrome and it doesn't work in that either.
After seeing the "Update Java" image, I decided to just play games instead of practice. Games worked fine. Then I really wanted to practice... So I checked my Java version, which was at version 6 29, and the current version is 6 31. So I updated to 6 31. Now when I check my version at the Java site it says I have the latest version, but the "Update Java" image still appears on the Snooker login screen, blocking the "Practice Mode" link.
I agree with sanschichis - please, developers, move the "Update Java" image so it doesn't block the "Practice Mode" link.
And I don't want to have someone tell me I should practice by playing games against people. If i'm playing a game, I have to wait usually 20 seconds for the other player to shoot, or 40 or longer if they keep making shots. In practice mode, I can just shoot shoot shoot, and get a feel for the table, and then I do much better and have a lot more fun in games that day.
P.S. I wonder if there is a link I could just go to to get to practice mode, in the meantime.