If it's a .co.uk (or .org.uk) domain, then I'd recommend 123-reg.co.uk (if looking at others, should aim to pay under 10 quid for domain registration).
daily.co.uk is also used by some (have not yet tried them myself) and seem low cost. I tend to get hosting separately in case of any disputes over fees (or a sudden increase, as happened one year... by keeping the registration separate I could switch to another hosting firm by changing one of the settings in the domain registration control panel).
If you're after something like a .org, .com or similar, there are plenty of competitive prices. I'd check GoDaddy.com, MyDomain.com, Name.com and NameCheap.com Prices range from around $8 to $14 per year for .com, org, net, info (though sometimes there are deals hence worth checking a few competing services).
Rather than pay standard 'renewal' fee, look around after 6 months for any 'transfer' discounts, they add a year to expiry date when transfer completes, and it's usually 20-50% less than paying most renewal fees.
Lots of options for web hosting, and e-mail, and it should be quite easy to provide you with e-mail forwarded to some suitable account (eg GMail as NN has suggested) while having web site on wordpress.com if that's what you decide, or using web hosting...
(I host for clients) and there are freebie packages (to set one of these up usually requires a two or three page web form to let you enter your name and mail address, site description/name [a longer form of what your chosen domain name stands for] and a few other details).
There are free photo galleries, blogs, etc available for installation, and it costs nothing but some of your time to try different ones out until you are happy.