British Museum, Tate Modern level 6, V&A cromwell road, and National Gallery trafalgar square all have genuinely fast free wifi. Password usually printed on entry tickets or available at info desks. Speed tests show 15-25 mbps consistently.

Tate modern's café on level 6 has laptop-friendly tables with charging points and thames views. Much better than paying £5 for coffee just to use café wifi on the south bank. V&A café gets busy 12-2pm but quieter after 3pm.