I’m really sorry, I don’t feel qualified to answer this question, because I don’t have enough direct experience of any of them. But please bear with me and let me tell you what I think you should look for in a Pilates instructor if you have a pre-existing lower back pain or sciatica.
You should almost certainly be starting with at least a couple of one-to-one sessions to make sure the instructor has a good working understanding of your limitations so that he/she can bring that to any future classes you may attend.
A good understanding of pain
This can be summed up in my Number 1 Rule “Use it or Lose it, But Don’t Abuse it”, of which there’s a good fleshing out in the article “What’s the quickest way to fix my lower back pain / sciatica?” In fact, you may wish to point any instructor to the article. If they show willingness to learn that’s a good sign. If they give off a “Don’t you think I know my job?” attitude, perhaps best to give them a body-swerve.
If he/she doesn’t accept what you bring to the mat, but tries to get you to fit in with their class, again this is a bad sign. Any good instructor should be tailoring the session to the needs of those in the class, including you. However, if the instructor takes you to the side at the end and explains that he/she can’t give what you need, that is probably a sign of a diligent, well-meaning instructor too! Hopefully you’ll be directed to someone more suitable.
Personal experience of pain
I’ve found that clinicians with significant personal experience of pain tend to make better clinicians. I’d bet the same is true of Pilates instructors. I guess this boosts empathy.
If you know of any Pilates Instructors in Edinburgh who specialise in lower back pain / sciatica and are worth a mention on this page, please feel free to comment, and I’ll try to make time to check them out on the above points. Meantime, just outside Edinburgh – in Haddington – is a fabulous pilates studio run by Maureen Evans called Complete Movement. She ticks all of the above boxes, and I’d highly recommend her. So, although Haddington isn’t quite Edinburgh, I hope I’ve delivered on some of the intent in this article. 😉 Please don’t take this as criticism of all the Edinburgh Pilates Instructors, it’s just that – as I said in my opening paragraph – I don’t know any of them well enough to give them my personal seal of approval.