Getting full access to the server is beneficial as well as harmful also. You can mess up all setting by mistake if you have full access. You cannot do such stupid thing in Shared Web Hosting.
Another thing you need to consider is the facilities and the features of the cheap web hosting plan you want to buy. For example consider the following; will my site be available for my visitors to see and access at any time and any day of the week? Will I get up to 99% up time as a minimum requirement for hosting my site? Do not just jump at any web hosting service just because it is very cheap without considering the facilities on ground. Search carefully for what you want.
Just because you have used Affordable Web Hosting doesn't mean it has to be poor quality hosting. There are lots of very good quality hosts available at very affordable prices. Also be aware of what comes as standard with your hosting and what comes as paid extras. Check that your potential host uses a popular control panel such as Cpanel. Some hosts use free panels and although they work fine, if the time comes when you have to move your website to a new host, control panels like Cpanel make the process a lot easier.
Below are a few more but I could go into great detail and do not want to confuse you. If you have the time, look into all of them by using your favourite search engine and decide which is best for you.
Is the name you want already taken? Chances are this is a good possibility. Unless you hold the copyright on the name there is little chance you can get Shared Web Hosting UK it inexpensively.
There are other TLD's that are Global such as .com and .net and these tend to bee used by people or businesses who require a global presence. Of course this will also make them very sort after and extremely valuable.
My one bit of good advice is do not sign up with any server for a long period of time to start with. It will be cheaper in the long run but at first just sign up for a little while. Try before you buy, make sure that the service provider is able to meet your expectations. If it does, then sign up for a longer period and save money.