It appears that whatever the host did during their maintenance window at 07:00 UTC yesterday, broke something. But due to the caching we have on the site it didn't become noticeable until 12 hours later. This meant disparity between the latest data and the latest known good working conditions.
As with everything, there are compromises. I have had to install on a clean server from a backup to get any resemblance of a working site. That site has no SSL, no friendly URLS etc, and I've lost around a days worth of posts, however after working on it all day solidly, we are now at least live.
I will endeavour to put back the frilly bits once things have settled back down and I've had something to eat/drink.