Top things to do in London for 5 days beyond the usual

Going to London for 5 days in October with my partner. It’s our second trip so we’ve done the Big Ben/Buckingham/London Eye loop already. Looking to go deeper this time.

Specifically we love: weird small museums, proper pubs with history, live music that isn’t a massive arena, and food markets.

I’ve seen the Hunterian Museum and Sir John Soane’s mentioned a lot, anyone been? And is there a good “museum then pub around the corner” combo y’all swear by? Would love to just do that on repeat honestly.

Also any boroughs we should just wander with no plan?