There are literally dozens of carts that will serve the basic needs presented here. I would like to point out that, contrary to some other opinions expressed here, I would strongly consider a hosted solution. First of all, it shifts a majority of the PCI compliance burden onto them and secondly, they have to keep their software constantly up to date to avoid security risks. When you host things yourself, the entire security and PCI burden shifts to you and you also will be responsible for ensuring that you have the latest security patches (if any are even provided).
I have yet to purchase any e commerce software that wasn't totally useless a year later - even with the patches. By then, all of these companies have moved onto bigger, better releases. There's nothing like moving from cart to cart every year, always playing catch-up.
Since you are in the U.K., I'd probably go with Core Commerce as my cart. Unless you are selling only to North America and not the U.K. In that case, I'd pick Big Commerce. Both of those carts have tons of functionality (including mobile commerce) fully customizable SEO friendly URL's and, of course, all the meta title, description and header tag functionality anyone could ever want (don't they all have that now?).