It shouldn't have any real impact on what you're doing - i.e. nothing on the tourist trail will be closed but Monday 29th August is a public holiday in the UK so places are likely to be busy.
Here's what I would do....
Stay at the Trafalgar Hilton.
On Day 1 you can check in then take a walk down the Mall to Buckingham Palace. On the way back, walk up through St James Park to Horseguards Parade and exit onto Whitehall. Turn right and you can walk down past the end of Downing Street (where the PM lives) and on to the Palace of Westminster, which is what you're referring to as Big Ben.
On Day 2, walk down to Embankment and get on a Thames Clipper boat to Tower. You'll get another good view of the Palace of Westminster, the London Eye, the Globe Theatre, St Paul's Cathedral and Tower Bridge.
You can then get off, visit the Tower of London, then - if you're up for it - start walking towards Monument. There's a tower here that was built after the Great Fire of London. From there, walk North up Gracechurch Street to Leadenhall Market , then down Cornhill to The Bank of England and Royal Exchange. From here, keep walking along Cheapside and you get to St Paul's Cathedral.
One detour worth doing at this point might be to go up to the Museum of London which is a good insight into the history of the place.
After that point I would go to the South side of the Cathedral and get on a bus heading back to Trafalgar Square.
It would probably be too ambitious to then try to get to Amsterdam that night, but you could easily do it on the morning of day 3. It;s by no means a comprehensive plan for a trip to London, but would be one way of covering off the essentials.