Totally depends what you want to do really.

If you want to build your website without anything like dynamic stuff & database driven, forums etc... you can normally just stick with the webspace you got from your ISP combined with for example: a free .tk domain.

If you want php capability you might want to have a look here: Free PHP & MySQL hosting. Of course you could also combine these with a free .tk domain.

If asp is your flavour there are also free solutions for that online.

But maybe you can tell us what you are exactly planning to do so we can give you some more "directed" advice

I use Getdotted.com & Freeola.com
They're both part of the Special Reserve thing.
Getdotted sells the domains, Freeola hosts them - for free.

I was looking to use the site to display some of my art work and writing that I have done along with a few other non discript things.

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by Freeola
FREE domain hosting for domains purchased at GetDotted.com
FREE unlimited e-mail addresses and e-mail forwarding
FREE unlimited web space to create your own free web site
FREE PHP, CGI & SSI to allow functional engaging web sites
ZERO ads, banners or annoying popups on your web pages
FREE web site promotion at Freeola Customer Sites
FREE sell your domain facility at TopAddress.com
FREE easy to use Control Panel to manage your Freeola account
FREE customer support from technicians (not premium rate!)

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Domain names are dirt cheap. You can get a .co.uk name registered for pence. Just make sure that it has your name as the registrant. the likes of www.123reg.co.uk or www.easily.co.uk can sort you out. You can set them up to redirect to wherever you host from. If you only want to display images etc, don't forget that most ISP's provide some server space, typically 10-25meg. This probably won't have any server side stuff like php/asp but if you don't need it then why pay for it?

Thanks everyone for the help, it's very much apperciated