IIRC the portrait place (which had music and stations set up to sell wine) on Thursday and the art/design major museum in Knightsbridge on Friday, when they were also open all night to allow more people to see a special exhibit (that was not free and was sold out at all hours). There were others and, in fact, I had the impression that most of the museums were doing this one day or night a week, but this was summer. The London transit museum did not have any free times and, in fact, the only way to get tickets within the next week or two involved joining for a year and making a donation.

Some of them are listed in tourist publications (like Where or What's On) with museum hours. I think google will product a couple articles with partial lists.