Hendon is awesome, but if I had to pick only one thing it would be Duxford. I've been there 4 times and have enjoyed it tremendously every time. Get to a bus station (via tube, to adhere to the spirit of your restriction) and take a ride to Duxford. You'll be glad you did. An easy day adventure and you'll be home early in the evening. I don't know where you are staying, but at the Victoria Station bus terminal you can take a bus that will drop you off and pick you up at the front door to Duxford. Just take the earliest departure so you have enough time at the museum.
Of course, there's WIXer Jason51 at Bottisham just down the road, but they're not open 7 days a week. Not yet anyway
Whatever you do, you can't see everything within reach of London, even if you had 48 days.
Enjoy, and we expect a book report when you return...with pics!
Chunks