Regarding unlimited web hosting, unfortunately a lot of people still fall for that marketing technique, but there's no such thing as unlimited web hosting.
If you're looking at a web host that offers unlimited resources you'll want to carefully check the terms and conditions. You'll likely find that your usage is then aggressively limited through inodes and low CPU and memory usage limits. Every file, including emails, count toward an inode limit. So if the host imposes these you can quickly find you can't upload new files to your "unlimited" web hosting because you've got a lot of emails.
So you'll often find that in practice you can actually use far greater resources with a host that has honest web space and bandwidth limits than one that claims "unlimited" resources.
Inode limits are definitely something to be avoided. "Unlimited" web hosting is a dishonest practice, and there's no such thing really. Any provider claiming unlimited resources is likely massively overselling their service as well, which can lead to poor and unreliable performance, slow loading times and poor support, as they'll likely be cramming far too many users onto their servers.
Regarding Fast hosts, we've moved a lot of users from their services, which are anything but fast. In fact we've found them perform worse than other well known poor providers such as 1&1 who also market heavily. A member we helped recently was getting up to 20 second load times for a simple WordPress website:
http://www.ukbusinessforums.co.uk/threads/are-fasthosts-slowing-down-my-site-loading-time.351336/
Webhostinguk will likely perform better, but in our dealings with them for example to migrate a website to us, they fall well into the category of broken English provided by outsourced support. You can also live chat to the same person at one of their other websites, and they won't even acknowledge that you're typing to the same person, it's bizarre:
http://dansgalaxy.co.uk/2011/04/23/why-webhosting-uk-com-sucks-part-1/
If you send an enquiry to a web host you're interested in that'll quickly give you an indication of what they'll be like to use; for example the speed of the response, and if its given in proper English. The very large hosts will likely respond slowly, and some of the other names given will likely not respond in proper English. If you then wanted to discuss something beyond basic day to day technical queries, you'd likely have difficulty with those that don't have proper UK staff and support.
For a UK business, it can be invaluable having proper UK based support where you discuss the best approach, platforms and tools to use to make the most out of your website and really drive your business forward.