I had 18 months of art therapy with a Jungian psychoanalytic approach. This was many years ago and I would be doubtful that such an opportunity is available now as CBT and other short term, outcome driven interventions are so wide spread.
It was an excellent experience for me. It introduced me to working with metaphor and archetypes which has remained with me. It felt like a solid introduction to my long term therapeutic work. I was indifferent about the therapist, although he was good, and relational stuff was not a noticeable part of the work.
I work with someone privately who is a Gestaltist and very relationally focused as well as having an emphasis on attachment. She's excellent and is well known in her field. I wouldn't have the emotional capacity and awareness for working with her if I hadn't had my previous NHS experience, or at least it would have taken me a long time to develop that. I don't believe I would be able to access someone like her working in this way through the NHS (due to systematic underfunding which of course is not the fault of the NHS).