It make much more sense. Over all, still leave a lot of time travel/rest, not as much time to explore.
Since you have time, you want do a little more research, to optimize the route.
For example the day 3, it would make more sense to go:
Changing the guard at Buckingham Palace , Hyde park, Piccadilly Circus, Trafalgar Square
or even ( make sure what time is the change guard )
Hyde park, Changing the guard at Buckingham Palace , Piccadilly Circus, Trafalgar Square
the idea is go one direction, not back and forth.
Also listen to other friend's suggestions, create your best vacation plan.
