You could easily register your own domain ( under 2 pounds if you go to www.GoDaddy.com and register somename.INFO ) or use a firm like 123-reg.co.uk and get your own .co.uk or .org.uk
(If the plan is for it not to be commercial, but, for example, a self-help group's forum, you can opt to not have your details online for .org.uk or .co.uk but .org.uk seems most appropriate - it's called "WHOIS Opt Out" to do this).
Web hosting can be had on Ebay for under a tenner a year. If you look for web hosting which mentions cPanel and includes Fantastico then you should find a number of forum options, probably including phpBB.
I'd suggest using a directory like "talk" so you can then have a sub-domain which will allow you to have a semi-private forum where spammers won't try to bombard you with membership requests and post adverts.
So assuming you registered a domain aselfhelpgroup.org.uk and posted a 'private' page for that (something like:
private pages
You need to know the exact URL to view pages here.
Goodbye
a fairly polite "go away" notice - see images.web-hints.info/ for my original page!)
Then you could let people know to visit your forum on 8talk.aselfhelpgroup.org.uk/* (which would be done via word of mouth or e-mail, so spammers would never find it).
Unfortunately, on some types of forum, spammers will try to flood the site with adverts for all sorts of other websites, including porn, viagra, and so on. You don't want to find you are bombarded with 'new user' requests or getting rid of spam, so 'hiding' the forum might be worth considering.