There are a lot of things to consider when considering Web Design Companies.
One of the great advantages of the internet is that you're no longer restricted to find a service in your locality. This is particularly true to getting your Website Designed,
Although having the whole of the Uk (or even the world) to choose from, it can be better to choose a company / freelancer that's geographically nearer to you, as it's always useful to meet the person who's going to be doing your work, especially if there are things that maybe difficult to communicate by phone or email.
Things to look out for.
Cost
This can vary greatly, generally the bigger the agency, the more it will cost. Using a bigger firm will pretty much guarantee you'll get a good site, but that doesn't mean that a cheaper / smaller firm won't be able to just as good a job, at maybe even a quarter of the cost.
Hosting charges - The cost of hosting has shrunk in the last few years. Some companies still charge around £25 a month for hosting your site. This is far too much. You should be able to get your site hosted for less than £10 a month. If you find your own host this would be even cheaper. You can give your web designer access to your host to build the site there. Doing it this way can cost you as little as £5 per month.
Although Web Design is a 'modern' type of business, all the old rules still apply. This is particularly true of getting recommendations. If you've been recommended a certain Designer, then it's always worth following up.
Important factors to consider
A content management system. This is where your website has its own login, and you can add to and edit your current website. If a web designer doesn't offer this don't even consider it.. Most good web designers now offer this as a standard part of their package. If you don't have a content management system / or access to it, you will have to pay a web designer every time you need to make a change to your website, which is obviously not a great thing to do.