With that sort of budget, it could be worth looking at the secondhand market, or on ebay. Lenses can be quite expensive...
You would quite likely find some good deals on the 70-200 f4. Since the f4 IS version came out, there are plenty people selling the older one - which helps to drive the price down.
A good option in fast lenses might be the 100mm f2. That should be quick enough for decent action shots, including in the UK. It's a little more than $300, but not that much:
http://www.adorama.com/CA1002AFU.html