The original GBBO support number 0800 500 3123 and GBBO FAQ help page have now stopped working.
Find a local website developer / website promoter who can give you advice and support. (you will drown on your own)
As mentioned, look at Wordpress.org for a website template.
Remember; anyone can create a website, but few can make it successful. You require many skills to make a website work. Over 80% of DIY websites will never be seen by potential clients, as the web is extremely competitive. (imagine a high street where every shop is selling the same product - that's how every Google search works.)
Might also consider looking at www.GBBO.co.uk (Get British Business Online) which has some free tools from Google hosting and may be free or cheap (it was definitely free a couple of years back, but obviously there'd be costs for renewing the [.co.uk] domain name).
If you prefer some other domain name (eg .com) then a US firm would be cheaper than most if not all UK registration firms. GoDaddy, MyDomain.com, Name.com, NameCheap.com all worth a look.
If you have a Windows PC then for designing pages, for free, you could use an older version of Netscape browser (it came with WYSIWYG page design built in). It may depend on what version of Windows you have as to whether you can get an older version, however. Message me if you want to go down this route as I can check what copies of Netscape I have and give some help.
When you say Design It Yourself, with what will you be designing? If you are going to use Dreamweaver or something like that, then that may determine what type of hosting you need, such as Linux v Windows/ASP, what database platform you need such as MySQL v MsSQL.
Tsohost and 34sp I have used. They will provide hosting space which you can then do what you wish with (within reason). You can install Wordpress or something like that if you wish, or purely upload your own html and css files.
I need to design a website for a small business (am self employed). I would prefer to only pay for hosting, and to try to get a cheap domain, and design it myself. I have looked at Weebly (which seems fine, but need to get a domain elsewhere), and 1&1 hosting. Are either of these any good? Or does anyone know of any others?