You've probably already got the web space available to you. Almost all ISPs provide their users with free web space. (The amount is usually quite generous. My own ISP offers 50Mb; that size should be more than enough for your needs). So, check out your ISPs website, to see what's available to you.
The only slight disadvantage of using the free webspace from your ISP is that you won't get a very snappy URL. Your site's address would probably be something like myisp.co.uk/members/p/pitstopbunny. However, it only costs a few pounds to get yourself something like pitstopbunny.co.uk . You still use the free webspace provided by your ISP but you have the traffic from the snappier address re-routed to it.
There are also plenty of free web-hosting sites. The downside of using them, though, is that they usually add advertising material onto your page. The content of some of that advertising might not be to your tastes. For example, if you were designing a site for your local church group, advertisements for hard-core porn sites might look slightly out of place! ;-)
Chris