@not just link spam
"I read this to mean that there wasn't a public forum that got spammed. Server got compromised and a forum installed to be used as a link dump".
Absolutely. It is not clear what happened on some of the other sites. Worcestershire seem to run a bona fide forum which just got link spammed. However, West Wittering don't.
They were thinking of setting up a forum - possibly this will put them off. So in effect, the hack used an exploit to get on to their server and then either installed a forum of its own or activated something that was there but unused.
If you looked at the site structure (before they took it down) there was very clearly a spurious directory that got added some while after the main site was put up.
That is one of the reasons for looking at this more closely. Link spam? Not much of an issue. Spam sat on .gov.uk domains may be a bit more, since it implies a lack of moderation on some government sites.
But exploits that colonise your site from within are something that fewer people are aware of, and also denote an attack that is just that bit higher up the malware food chain. Of course, one solution is to do a regular check of your own site for "+porn"... which will work fine unless you site happens to be a porn site.
Then you might have problems.