I seem to remember a Sky Bet app coming out for WP8, then people were saying it disappeared from the store. I presume Sky pulled it. Anyway, I don't actually use it myself, but a friend of mine uses Sky Bet on Windows Phone and the mobile website works well for them and they use m.skybet.com. Just tried it on my phone (Lumia 920) and it works fine as well, including the Login button.
Can't see any reason why it shouldn't work on your 925. You could perhaps try clearing your history and cache to see if that solves the problem. You can do this by tapping on the 'delete history' button in IE's settings. However, this will also remove your history and any saved passwords you have in IE on your phone, but if that's not a problem for you, then I'd give this a try to see if it gets it working.