The actual name of your domain will not directly affect where your site appears in the Google rankings but there are a few things you can do to improve your ranking:

First of all, if your customers are in the UK and you are searching for your domain on www.google.co.uk your site will rank higher if it is a .uk domain than if it is a .com domain for example. With this in mind it would be worth owning the .uk version of your domain (if available).

By far the best method of improving your Google rank though would be to register with Google for their Webmaster Tools. This will (among other things) allow you to verify your domain with Google and also generate a site map file which will help Google index your website in their searches which will gradually increase your Google ranking. If you have a Wordpress website there is also an additional plugin you can install which will generate the site maps for you called: Google XML Sitemaps