I think I've finally got search working how I want — it's only taken 10 months. 😆
Now, a post should only be included in the results of the search term appears in the post content and not just in a link.
I also thought that it was a bit annoying having to scroll to the bottom when wanting to go to the next page of results so duplicated the pagination at the top. Fortunately, it was just a case of copying the block of code and changing one piece of CSS.