Add the London eye to the buckingham palace dAy (I assume you are going in august when they are open? ). The eye is a quick walk across river and in summer has long opening hours- actually it will fit around any day you have planned.

I would go to the tower of London from Westminster pier on a red river boat or all the way to grenwich of you have time.

To go into parliament I think you need to be invited? Walking past takes a few minutes.

Where are you staying?