As others have said, you need to do a lot of cutting. First, have you been to London before? Or, have you been to Europe before? Are you flying directly to London or will you be touring another city beforehand? If London is your first stop, and this is your first European trip, you don't know how jetlag will affect you. You say you arrive Tuesday afternoon - it will probably take you at least 3 hours to get out of the airport and to your hotel. Then it will be time for dinner. Then you'll most likely be really tired and fighting sleep. So don't plan anything timed or ticketed that first day. If you manage to make it out, do a walk or something minor, not a major must-see sight.
Read Rick's London book if you haven't already--it's great. Note that London is not known for its wines. Consider a brewery or gin factory instead. Or just drink the local sips in a pub. To me, if this is your first time in London, visiting a booze-making venue is going to take the place of some very other top-notch sites that might be more worthwhile.
As others have said, the British Museum and V&A can each take a full day. Don't underestimate the amount of walking you can do just inside the museums. Similarly the IWM is enormous. Plan no more than 2 big sites per day. Like:
Day 1: Westminster Abbey and Churchill War Rooms.
Day 2: Harry Potter
Day 3: British Museum and Tower of London (but this will be exhausting)
Day 4: V&A and something else....
I would NOT plan two museums in the same day, you'll get museum fatigue. Even though the Tower of London is technically a "museum" of sorts, there's a lot of it outdoors and it doesn't feel like a museum.
I last went to London in 2004. Here was my itinerary, and here's what I actually got accomplished:
Day 1:
7:30 – Arrive
9:00 – Get to Victoria Station, put bags in locker; catch Original London Sightseeing Bus
11:00 – Hop off bus @ Buckingham Palace
11:30 – Changing of the Guard
12:30 – Lunch in Covent Gardens/people-watching
2:00 – Cruise on the River Thames (leaves from London Eye; including in above bus price)
3:00 – Westminster Walk (see Rick Steves’ Guide) – actually go in Westminster Abbey and Cabinet War Rooms in addition to walk
5:30 – Head back to Victoria Station ; get bags; go to hotel
6:30 – Dinner and rest
(On this day, we mostly stuck to the schedule. We did not do the sightseeing bus as we got lost in Victoria Station. We were very tired and had to fight to stay awake, dragging around all day.)
Day 2:
This is the day it started falling apart, haha!
9:00 – Tower of London (Beefeater Tour, Crown Jewels)
12:00 – Head toward Tate Modern; lunch
1:00 – Tate Modern
4:00 – Vinopolis, The City of Wine
5:00 – Saint Paul’s Cathedral
6:00 – Head back to hotel; quick dinner/rest
8:00 – “Phantom of the Opera” in Theater District
We did the Tower sans Beefeater tour, I forget why we didn't. Maybe got there late? After Tate Modern we were too tired to do either Vinopolis (which is now closed), or St. Paul's, or Phantom. There was a LOT of walking at TOL and Tate.
Day 3:
10:00 – Imperial War Museum
12:00 – Lunch in Trafalgar Square
1:00 – Walk to Piccadilly Circus; people-watch
2:00 – Harrod’s
4:00 – Speaker’s Corner; walk through Hyde Park to get there
5:00 – Tube to Abbey Road; get Beatles’ picture crossing street
6:00 – Dinner; back to hotel; laundry; pack/rest
We didn't make it to IWM as husband thought he lost his passport and we spent the morning looking for it. Couldn't find Speaker's Corner in Hyde Park.
Sooooooo....as you can see, what you PLAN to do can be quite different than what you ACTUALLY do. Since that first trip, we have planned at most 2 things per day. And if we have extra time and feel like doing something else, we do it. And if we don't....we don't.
Oh, and I'm going back to London next year and will catch St. Paul's, the Imperial War Museum, plus some other things I missed. Assume you'll come back.