It will have been a long flight and by the time you get through collecting luggage, customs and to your flat it could be 6pm or later. I'd unpack, then head out to find a spot to eat in the vibrant Bayswater neighborhood. Loads of options on Queensway or Westbourne Grove if you are in that part of Bayswater. If you are closer to Paddington Station, Tukdin Flavors of Malaysia on Craven Road has good food for a good price. Could then simply walk around your neighborhood until you're ready to get some sleep.
On Sunday morning get an early start and take the Tube to the Westminster stop. From the Bayswater neighborhood you'll most likely be taking the Circle or District line to Westminster. Exit at Westminster, Mind the Gap and follow signage to EXIT 1 (Westminster Pier, London Eye, Westminster Bridge), walk out the exit. In front you is the Westminster Pier (where you can catch a boat for you Thames trip later), the Eye is across the river to your left, the bridge to your right. Turn right and look up. Smile, climb the steps and begin your day at Parliament Square. From here you can wander over to the Churchill War rooms (make sure what time they open on Sundays) or see Westminster Abbey (again check schedules, services may preclude you from entering unless you'd like to partake) or do both. Going out on a limb and saying WWII history is of interest to you so might I suggest visiting the Imperial War Museum (if the renovations have been completed, they say July but who knows). You can tube to Lambeth North, then walk from there. From here you could tube back under the Thames and visit Covent Garden, Trafalgar Square, Leicester Square, etc. Late lunch then your river cruise.
On Monday I'd be the first people in line at the Tower of London. From the Tower off to visit Leadenhall Market and from there to St Paul's. Nice lunch and depending on your stamina maybe a visit to one of the many free museums or back to the apartment for a nap so you won't be tired for Les Miz.
Someone can correct me on this but if you wanted the full Portobello Market experience I believe you can only find it on weekends. Otherwise it's mostly fruit and veg stalls during the week. Haven't been in years so please check their website for hours and days.
Camden Lock Market is great and a walk along the adjacent Regent Canal lovely sojourn.
You can see a lot of London in 3 full days. Simply have to map out what's close to what, your must sees and head on out.
