That's a tall order, even if your first day isn't jet-lagged after an overnight flight. Your targets are at opposite ends of the city and on both sides of the Thames, so you'll spend time getting to and from them. Big Ben/Parliament is a walk-past sight that won't take long, you could visit there the first day. I'm a big fan of the nearby Churchill War Rooms, and there's lots to see in that area -- Whitehall, Trafalgar Square, Buckingham Palace, etc.
The Tower is a unique sight best appreciated in the morning when less crowded, maybe your second morning as soon as it opens. Take the Yeoman Warder tour and skip the crown jewels. Then maybe the British Museum for as long as you want that day. I'd say skip the Imperial War Museum on this trip unless it's really important to you.
Don't try to get to all these places on foot, they're too far apart. But you'll have time for some walking near them -- the City near the Tower, Bloomsbury near the British Museum, Whitehall and Mayfair near Churchill. And whatever neightborhood your hotel is in, of course. Hope that helps.
