It's a well trodden path but the answers aren't always the same.
The Canon EF-S 15-85mm f/3.5-5.6 IS USM is the first lens I'd recommend which fits your budget.
It's much sharper than the kit lens, it focuses more quickly, quietly and consistently as well. It also has the benefit of featuring full-time manual focus. It is much heavier than the kit lens too but you should become accustomed to it fairly quickly.
There is the 17-85mm, which is the predecessor to the 15-85mm to consider as well. You can get decent used ones for less than £200. The reason why I ruled it out is that it suffers noticeable distortion at the wide angle, even when you stop it down.
There are also the 17-50mm f/2.8 offerings from Tamron and Sigma to consider too if you're looking for something that works well in low light. However they are reportedly inconsistent in terms of optical quality - some people have claimed they've had to buy and return several copies of the same SKU to get one that was optically sharp though you may fare more fortunately than they did.