Originally Posted by flatlander

I know you stated a lack of intention to make a daytrip, but I should add that several places outside London are reachable by a train journey of about an hour, in case this had not occurred to you. So it is eminently possible to visit them with about as much ease as visiting the more distant parts of London itself. For example Cambridge and Brighton can both be reached in an hour. If the thought of difficult driving or poor transport links was putting you off, then this is surmountable. Once you are in Brighton or Cambridge they are very walkable. Of the two, if you want to leave London, I recommend Cambridge, because I don't think Brighton is that much fun in October.

Originally Posted by ajGoes

Speaking of the London Transport Museum, you should prepare yourself for two kinds of sticker shock at London museums: shockingly high and amazingly free. I had an out-of-date guide that listed what I thought was a reasonable admission fee, £8 IIRR. When I arrived at the museum I was stunned to discover that daily entry passes no longer existed. Only annual tickets are available, at £16 a pop. It may have been even higher when I was there in 2013.

I couldn't bring myself to pay US$50 for a couple of hours' browsing for two, so my wife and I proceeded to the free Victoria and Albert Museum.

The V&A, British Museum, National Gallery, National Portrait Gallery, Natural History Museum and many others are free, though I always drop a few pounds into the contribution slots. Non-free museums are almost universally very expensive. You're spending a lot more money to get to and stay in London, so these costs don't really increase your total expenditure all that much percentagewise. They'll feel less like a punch in the gut if you're expecting them.