Most of my standard recommendations for quirky London museums have already been mentioned: the John Soane, the Huntarian, the Old Operating Theatre, the Museum of Docklands (am meaning to catch their current Siege of Sidney St exhibition) and the Cartoon Museum. Nobody’s mentioned the Wellcome Collection, but it’s fairly high profile.
Having seen them in the last year or so, I might have mentioned the Canal Museum and the Royal London Hospital, but you’ve already ticked them off.
I’m not sure I’d normally recommend all the following, but at one time or another I’ve done most of the science-y museums in town. Omitting the big ones:
[ul]The Faraday Museum in the basement of the Royal Institution. Overhauled in the last couple of years to give a contemporary spin on their historic collections (Tyndall and the greenhouse effect, etc.), rather than just have the reconstructions of Faraday’s labs. These days you also get to explore the rest of the building.[/ul]
[ul]The Franklin Museum. His town house in Craven Street, behind Charing Cross station. Saw this on an Open House weekend a couple of years ago when they weren’t doing it, but normally seems to have a heavy actors-interacting-with-visitors component. An interesting example of a small 18th century house, but I thought the best bit was the basement about the anatomy school that had been next door. It’s the unique example of 18th century anatomy detritus turning up in an archaeological dig, with lots learnt from it.[/ul]
[ul]The Grant Museum in UCL. Comparative anatomy, so a roomful of skeletons and fossils. (Grant was a major influence on the undergraduate Darwin in Edinburgh and the museum is almost exactly on the site of the house where the latter hit on natural selection.)[/ul]
[ul]The Petrie Museum. Also at UCL and literally round the corner from the above. Egyptology. Mainly lots of pots, arranged chronologically to teach students how to date Egyptian pottery fragments. Dry, but oddly satisfying.[/ul]
[ul]The Freud Museum. The shrine in Hampstead. Relatively expensive for what is essentially the single preserved room. But what a room.[/ul]
[ul]The Brunel Museum. Pretty much a single room, but a nice explanation of how the father and son engineered the Thames Tunnel.[/ul]
Suspect you may have set yourself a hard target if you restrict yourself to London proper, particularly if you exclude art galleries and the like. The Wiki list you link to on the blog looks thorough, but once you start excluding stuff that’s currently shut or difficult to get into, that list begins to shrink.