At one time you had to travel across London to find a yoga class. But nowadays there are so many yoga instructors in London that no matter which part of the capital you are in you will have a choice of teachers and classes covering a variety of styles of yoga.
If you don't know where your local classes are, there are various websites for finding classes. The British Wheel of Yoga (the largest yoga membership organisation in the UK) has a class finder for its members. You could also try Class Finder.
The Satyananda Yoga Centre, Balham is one of the longest established yoga centres in London, having been founded by Swami Pragyamurti in the early 1970s, who still teaches there. The centre offers hatha yoga classes but also places an emphasis on the deeper aspects of yoga such as meditation, pranayama and mantra.
For one-to-one tuition get in touch with Hakan. He is a certified Jivamukti Yoga teacher who has practiced yoga and meditation for since the 1990s. Hakan has taught yoga at Cambridge University and numerous companies and orgnanisations for years and and offers private tuition around London tailored for lower back problems, stress, shoulder and neck issues and classes for athletes on a one-to-one basis.
For those wishing to go deeper into Yoga a retreat far away from the hustle and bustle of city life is invaluable. Mandala Yoga Ashram in Carmarthenshire (Wales) is an idyllic retreat situated in a commanding position with spectacular views overlooking the Llansadwrn valleys to the Beacon Beacons beyond. Since the mid 1980s the ashram has provided a quiet, safe and peaceful haven in which to further yoga practice and understanding, and bring about inner discovery and awakening. The spiritual head of the ashram is Swami Nishchalananda who has studied and practiced yoga and meditation for 50 years.
For yoga supplies, Yogamatters has a great choice of mats, clothing, equipment and books (a wide range of Satyananda Yoga books especially).