Of course.
It sounds as though you’ve considered this carefully. It will serve you well to clarify your intentions as much as possible. That clarity will allow you to find what you are looking for without getting sidetracked by other “stuff”.
For healing, Yoga takes a three-prong approach; asana/pranayama, meditation, and lifestyle/nutrition. Any one of the three may have a degree of efficacy for this or that. However if you are hoping to have your back issues go and not return (rather than leave temporarily) then this approach is imperative.
Some of your starting may depend on your location - which appears to be a bit south of London in the UK. Please find and contact Drew Stallcop. He is an amazing teacher, certified in Purna Yoga at the 2,000-hour level, and well versed in therapeutic work. He’ll also know the area far better than I.
If you choose to go on your own instead, please look for an alignment-based teacher with therapeutic training, several years under their belt, who has a sound teacher themselves, continues their training, AND lives what they are teaching.
gordon