Best days for London sites

I don't think that the day of the week matters much except for certain markets. I haven't been to Burough Market, so don't know what days it is open. Some of the museums have 'late days'- days where they are open until 8:00 or 9:00 pm, so I'd suggesst checking that out also. Most theatres are closed on Sunday and some have matines on various afternoons (often Wednesday or Saturday)as well as the evening shows.
In my opinion, the better way to organize things in London is by location. I'd plot the locations on a map and check out transportation between them. Then group them as needed. The Tower will take from 2-5 hours- so allow at least 1/2 a day for it. The British Museum and British Library can take days- or just a short time. It depends on what you want to see and how 'effciently' you see things- sometimes we like to move right along and other times we 'contemplate'. I'd make Kew a high priority! It is one of my favorite places in London. It can take 1/2 to a whole day. There are several greenhouses (some very old, one dedicated to Diana rather new), a small aquarium, different 'gardens', a redwood forrest with a 'skywalk', several buildings..... in other words- lots of wonderful stuff. And the shop there is marvelous- on of my very favorite shopping places (the shop at the Tower of London is also very good). I don't see Windsor on your list. It makes a nice 1/2 or whole day trip. Both the castle and the town are excellent. We often go to Windsor on the day we have theatre tickets for the evening. Be aware that St. George's chaple is closed to tourists on Sundays, though.

Agree with Toni. Group what you want to see together. You mentioned you are staying near the Abbey which means you'll ALSO be close to Parliament, Big Ben, Cabinet War Rooms, Horse Guards, 10 Downing street and if you cross Westminster Bridge, the London Eye. Few more blocks the other way and via Birdcage Walk you'll pass by St James Park on your way to Buckingham Palace. Personally I'd group the Tower and Borough Market together. http://www.boroughmarket.org.uk
Start in the early morning at the market, take pictures of the Beehive(London City Hall) walk across the Tower Bridge and visit the Tower of London. (you've made reservations haven't you? Cheaper to book in advance online) From the Tower walk up to lovely covered Leadenhall Market. Late afternoon lunch or early dinner. British Museum can take hours if you are really into Egyptology. http://www.britishmuseum.org/visiting/admission_and_opening_times.aspx The Treasure Room at the British Library (Sir John C Ritblatt Gallery) is easily an hour. The other excellent gallery collections will also take time. http://www.bl.uk/aboutus/quickinfo/loc/stp/opening/index.html From there strolling around or maybe enjoying a picnic in nearby Regent's park is a lovely way to see London life. Kew Gardens can be a day. You'll be surprised how much you can see in a day in London. Simply pace yourselves.

Tower - I'd suggest Monday or Tuesday morning. It is always crowded, but weekends are likely to be worse. British Museum - It is open late on Friday evenings. I've visited in the evening and found it much less crowded than during the day. Evensong - check the schedule as your choices will be limited. Borough Market - The only real option will be Saturday which is the day it is most crowded. Theatre - Sunday choices are very limited. Some theatres are also dark on Monday, but if there are shows you want to see playing that evening, that would likely be the least crowded day. Kew Gardens takes the bulk of the day. I'd suggest that you visit on Sunday as some sights have reduced hours on Sunday (but not Kew Gardens).

Go online and check the hours of each location. Be sure to check about Borough Market and when the vendors are open. You can walk around the market anytime, but it isn't much fun if no one is open. (BTW, "Southwark" is pronounced something like "Suth'ick", where "Suth" sounds like the first syllable in "Southern". There's a great cathedral there, too.) The Tower and the Museum will likely be the busiest over the weekend. But, not suffocatingly busy. They're used to it. From your hotel, you will have an easy walk to the Abbey and the Cabinet Rooms. The theater will likely be a few blocks north, through Whitehall. The rest will require the Tube. Westminster Station is across the intersection from the Abbey. Don't fail to walk across Westminster Bridge and check out the South Bank.

Go online and check the hours of each location. Be sure to check about Borough Market and when the vendors are open. You can walk around the market anytime, but it isn't much fun if no one is open. (BTW, "Southwark" is pronounced something like "Suth'ick", where "Suth" sounds like the first syllable in "Southern". There's a great cathedral there, too.) The Tower and the Museum will likely be the busiest over the weekend. But, not suffocatingly busy. They're used to it. From your hotel, you will have an easy walk to the Abbey and the Cabinet Rooms. The theater will likely be a few blocks north, through Whitehall and north of Trafalgar Square. The rest will require the Tube. Westminster Station is across the intersection from the Abbey. Don't fail to walk across Westminster Bridge and check out the South Bank.