The Fashion and Textile Museum in Bermondsey focuses on contemporary fashion, textile design, and the craft behind clothing. It does not have a large permanent collection on display in the usual museum sense; the draw is the changing exhibition programme, which can range from designer retrospectives to fabric, print, and fashion-history shows.
It is a good specialist stop if the current exhibition matches your interests. The museum is close to Bermondsey Street, so it pairs easily with White Cube, London Bridge, Borough Market, or a walk toward Tower Bridge.