When London rain sets in, I head to South Kensington. Two of the city's great museums stand almost side by side on Cromwell Road, both free to enter, and you can reach them without getting wet: a pedestrian tunnel runs from South Kensington station straight to their doors.
The V&A
Walk in through the main entrance and look up. The rotunda holds a huge chandelier of twisted blue and green glass by the American artist Dale Chihuly, and it is the best free welcome of any museum I know. From there t