A few suggestions, not museums but maybe ways of thinking about Victorians in a non-exhibits-behind-glass way:
A look at the Albert Memorial and a run around Kensington Gdns?
Baker Street station- first underground station built mid-Victorian era- still has big vaulted brick chambers etc underneath- and would lead on nicely to the Sherlock Holmes museum, which might be fun and pique his interest in detective stories.
Kew Gardens- all the glass houses and urge to globe trot collecting plants to put in botanical gardens is v Victorian in origin plus they have a fantastic tree top walk there at the moment, I've heard. Probably not Victorian but none the less fun... (In fact, I really want to check it out with my boys so if you fancy company on that one send me an email!)
Highgate cemetary to see Karl Marx's grave and ramble round. Or Brompton Cemetary is great for a peaceful run around- you can read all the old fashioned Victorian names together and note how they're making a comeback.
Any of the Peabody estates are great examples of Victorian philanthropy (built to provide "cheap, cleanly, well-drained and healthful dwellings for the poor" and a quick shufti at them can be combined with other stuff- Spitalfields market etc.
Tower Bridge is typical mix of new Victorian engineering and old architecture, I'm told. Lots of other stuff to do round there too- St Katherine's dock is Victorian and worth a wander round.
The vintage prehistoric monster collection at Crystal Palace sounds good and you can tell him all about the great exhibition.
Any of the big London railway stations are Victorian. Take him to the coast from one- all that day at the seaside stuff is very Victorian!
HTH.