This is cramming way too much in. I have been to London 3 times and still havent seen everything.
Like Rick says, always assume youll return.
What about getting the local feeling? Do you have time to just wander the mews and old neighborhoods and find the little corner pubs? If thats not your thing, fine, but if you really want to feel the heart of London, its part of it.
Day 1 is always the worst day ever, standing around waiting for the changing of the guard with jetlag and lack of sleep really sounds bordering on torturous to me. And its overrated. Same with Ceremony of the keys. Alot of standing around and waiting for things!
Think about the travel time between each thing. You would need to get to Buck. palace by 10 am at the latest to even be in the area to even see through the gates. Which would cancel out going to Churchill museum & War rooms since youd need to get on travelling by 9:30 to get to Buck. palace by 10ish. And youll be standing there waiting until 11:30. Tired, hungry, jetlagged and bored. Then itll still be a while for the sha-bang to be over.
Day 2 - The tower can take even an hour just to get a ticket for admission, then wait an hour or so just to get in and the tours can total at least 2, 3 hours at minimum. So if you do go at 9 am, you probably wont even be leaving it before 2 pm. I would scratch the Beatles walking tour and do it another time with your own map you can get off the internet.
Day 3 - British Museum. I went there 3 times for about 2 hours each time and have still just scratched the surface. Same with Harrods. HUGE area to cover.
SO this can work if you just want to tick a box to say Yea been there. But for a complete fulfillment, I think youre wayy to focused on the museums and galleries. Each of my trips I have saved something for next time becuase I didnt want to rush anything and not get the full enjoyment.