On Thursdays at 1pm there's an hour-long lunchtime yoga class with a lovely woman called Rosemary. The first class is £5 and you can just drop in. No need to bring a mat. It's a pretty cool church hall with stained glass windows. If you need to change you can sneak into the restrooms in the hotel next to Liverpool Street Station.
The Parish and Ward Church of St Botolph without 3TL, Bishopsgate, London EC2M, UK