The branding Liam has done for EE, and a couple of the guidelines to consider when designing the website.

To cater for the lowest common denominator it's advised to design websites at 800px wide so that people with older monitors etc don't have half the site cut off their screen, eliminating horizontal scroll bars. This means that the site doesn't take up the entire window. I think it would be best to keep it centered within the window with some sort of background behind. Here I've picked up on some of the colours/patterns that has been used for the printed promotional materials.

Using a photograph of some of their work as a header perhaps, with a drop down menu placed below that. Although it might be better to have the menu above it so that when it drops down, the only web content that is covered is the photograph. I also think it would be a good idea to have a welcome message on the home page which gives visitors a bit of an introduction into what EE do. This will then tap into the personal yet professional vibe that the company want.