The William Morris Gallery in north-east London has won this year's £100,000 Art Fund prize for Museum of the Year following a £5m renovation.
The Walthamstow gallery was praised for its community outreach and for "setting the highest standards of curatorship".
A second prize, of £10,000, went to the Hepworth gallery in Wakefield for its "world-class" education programme.
The winners were announced by Private Eye editor Ian Hislop on Tuesday at the Victoria and Albert Museum in London.
The recipients were revealed live on BBC Radio 4's Front Row.