Thank you everyone for giving me such a detailed answer to my question. I did a Broadband speed test and according to that my connection is "excellent" and I get download speeds of around 4mb/s. I was incredibly surprised by this because simple browsing does not seem as fast to me as it should (or as fast as I have experienced on other people's connections).
It makes sense what tg says about the download speed not being the complete story, and I am definitely keen to go for a more gaming orientated provider. Be seem to be a good option, and I think there is a consensus here that I will get a good service from them. They also offer unlimited bandwidth, which may come in handy as I have been hitting very close to my current limits.
Could I ask a related question. Are any of you gamers able to have another computer using the net without any noticeable effect to your online gaming? My girlfriend likes to browse the internet whilst I'm playing, but it almost always affects the performance, which is understandable but obviously very annoying. But I was wondering if it is possible to have a connection that could support both simultaneously?