Hi folks, just thought I would report back, as I managed to answer my own question. I found something called SimpleBlog
It did require database installation but that was pretty painless (plus the developer, Stoian, offered assistance if required), and the actual PHP installation was very straightforward.
Stoian was very helpful in modifying the script to provide functions I was looking for, such as categories for blog posts, allowing multiple blogs which show only the posts in the required categories. He provided this and some other modifications for a very modest fee, as well as responding promptly to other technical questions and requests.
If you want to see what it looks like within my HTML site:http://www.2bconsultancy.co.uk/blogland.php
I still need to add more posts, and also intend to make the three different blogs more obvious and accessible, rather than using the left-hand navigation, but the blog engine itself is working nicely. Stoian also produces other scripts to insert functionaility into static pages, eg forum, events, even simple page-based CMS.
SimpleBlog is highly recommend if you want to add a dynamic blog system to a static HTML website, without embarking on a major update to a Content Management System (CMS).
It's ironic that the answer to my question was the title of my question!