Reddit mentions of Body Control Pilates Back Book: A Training Program for the Prevention & Management of Back Pain

As you're in the UK, you may remember that when Pilates got some attention years ago the main variant that was all over the place was "Body Control" fronted by Lynne Robinson. You can see a lot of her stuff's been uploaded to Youtube. I tried it for a while so remember that her bio was that she had big back problems and she took up Pilates and actually got a few inches taller. Since you can't really grow in adulthood (despite what many dodgy websites say) it was mostly about Pilates straightening her spine which wasn't straight.

From what I've seen from online videos, not all Pilates is the same because Body Control seemed to put a greater emphasis on very strictly engaging the core muscles before doing anything and constantly lengthening the spine, so that particular version might be worth a look though it is a very slow and boring version. I see there's a specific Back book on Amazon by Robinson but know nothing about it.