I am a yoga teacher and have practiced Pilates as well. Yoga is good for all muscles in the body, and will strenghten the back and also release unnecessary tension which is often the cause of pain (Pilates is more about strenghtening abdominal muscles, but also helpful for back health, and is largely based on a selection of yoga postures). Yoga will also emphasise relaxation and stress relief, and depending on the teacher, breathing techniques and meditation and is more of a holistic practice. Yoga classes will range from very traditional, possibly including chanting, to a more secular, contemporary approach. In either case, make sure you go to an accredited, trained teacher and don't be afraid to quiz them about that their classes involve. For yoga, look out for British Wheel of Yoga teachers (postcode finder to find your nearest teacher on http://www.bwy.org.uk
) or the Yoga Alliance. Other BWY accredited teacher training organisations include Mandala Yoga Ashram, Satyananda (Satyananda UK-Ireland), Centre for Yoga Studies, Inner Yoga Trust, Yogacampus, The Yoga Academy, Triyoga, Sadhana Mala, London Yoga Teacher Training and the The Krishnamacharya Healing and Yoga Foundation. For Pilates, take a look at http://www.pilatesfoundation.com
Remember that it is not a legal requirement to be trained and anyone can set up as a yoga or pilates teacher so it is useful to use these resources and ask teachers about their training. There is lots of good teaching practice out there but also uninformed/inexperienced/untrained teaching practice.
Start with a gentle, slow beginners class if you can, or a small group class, for either yoga or pilates, so you can get the techniques right. Last but not least, you may well need to shop around, try different teachers. Classes, approaches and teaching styles can be vastly different in both yoga and pilates. It is important to find a class and teacher that suits you so you are more likely to enjoy it, benefit and stick with it.