On your fourth day, you could get in a walk through at Borough Market. It is in the neighborhood you are covering that day and you will not regret it. You could go there first, in the morning, as it is open 9 - 4 on Saturdays. One of my very favorite REAL places in London.
Then walk across the bridge to the Tower of London. It is my opinion only, but don't get delayed by the Tower Bridge Experience, which I have read (and I agree completely) is a 'poor value.' Just walk across the bridge for the views before visiting the Tower.

Thanks Cynthia! Good suggestion for my fourth day! Since you seem to have been through the neighborhood, any ideas for a place by the Monument I can sit and get something to drink after all those stairs?

Great way to start with the London Eye. I hate heights and flights but that was amazing. Will you arrive in time for tea on your first day before the London Eye?

Your second day might be a good one for tea since you won't need to spend as much time with Big Ben and Trafalgar Square as you might in a museum. I've enjoyed tea at the Hyde Park Hotel (which is under different ownership and may no longer serve tea), Fortnum & Mason, Brown's Hotel and Maids of Honour in Kew among others. If you are short on time and need to cut anything from your list consider the changing of the guard. It can be very crowded and difficult to see much.

Definitely go to the theatre--more than once if you can.

I am a librarian too and on my first trip to London got misty eyed when I realized I was in Poets Corner in Westminster Abbey and there was Chaucer's name was carved in an ancient stone.

If you are a librarian then you must visit Samuel Johnson's house.
http://www.drjohnsonshouse.org/

http://maps.google.com.au/maps?hl=en...ed=0CBgQ8gEwAA

Have drink at the Old Chesire Cheese Pub too if you are nearby. It is one of the oldest pubs.

HMS Belfast is well worth a look. The Old Bailey as well.

Not didactic comments:

Day 2--I wouldn't mess with bus tour. Get to Westminster Abbey as soon as it opens--a few less people in the crowd. You could probably go to St. Paul's after lunch.

Day 3--I think the changing of the guard is only in the morning and I hear overly hyped and not worth the time it would take you to get a good look, as you'd have to be there way before it happens to get spot. The Museum and Library will take your whole day.


Day 4--Go to the Tower at opening; go straight to the Crown Jewels. Then see rest. Then go over Tower Bridge and along the Thames to Tate and Globe. (If you have tickets for Globe, that's a different matter.)

Day 5--There are good tours, some thematic, of Oxford run from their Tourist Info office. Google them and see what they have on the day you are there. I wouldn't mess with a "tour" other than a walking one like they offer. Get a map, read walking tours on line, explore yourself. (We LOVED the Insp. Morse tour from the TI and there are Tolkien, Lewis, Lewis Carroll, etc. ones, so I WOULD recommend one of them, but not a whole day thing.) You can catch the Oxford Tube (NOT a "subway"/tube) or OxfordEspress which are coaches that you just hop on at a few spots in central London and ride about an hour and get let off in the center of town. Or there is the train. Either pretty cheap and pretty easy.

Oxford also has a HoHo bus that comes in handy if you just want to spend the day walking. Read Jan Morris's book on Oxford for atmosphere.

Westminster Abbey is pretty special.
The Tate Britain has always been my favourite (but haven't seen the Modern)
National Gallery, British Museum
I'm not a big fan of Buckingham Palace
If the weather is nice, a walk in the park on the weekend, if Sunday, Speaker's Corner in Hyde Park. Kew Gardens is also nice if the weather is good.
On Saturday, Portobello Market