Here is my suggestion for taking in the sites you want to see. It incorporates some of our favorite walks in London. And we actually have done most of this in a single day.
Start with the train from Marlow to London Paddington (52 minutes, one change on the way). From Paddington, take the Tube to one of the stations near Buckingham Palace on the Circle and District Lohnes—-Victoria Stations, or St. James. Whichever is on a direct Tube line from Paddington. (My choice would be St. James for the nicer walk through STL. James Park. Walk up and view the Palace from the front, then head toward Trafalgar Square, walking down the Mall or better yet through St. James Park on a path parallel to The Mall.
Once you have had a look around Trafalgar Square, walk east down Northumberland Ave. to the Thames at the Hungerford Brigde. The pedestrian Jubilee Bridges are attached on either side of the train bridge; take the one on the south side (your right as you face the bridge) and cross the river. Turn right and follow the pedestrian Thames Path along the river with great views of the buildings, including the Elizabeth Tower. Keep on past Westminster Bridge to admire the Parliament Buildings from this vantage point, then turn around and walk back, crossing over Westminster Bridge (the left sidewalk is less crowded with shell game conartists). Go have a look at Westminster Abbey before heading to Westminster Pier just north of the bridge.
Now you will board a Thames Clipper/Uber Boat for a ride on the river all the way to Tower Pier to see iconic Bridge and the area around the Tower of London.
From here you can get yourself back to Paddington by Tube, or #15 bus to Trafalgar Square then Tube, or boat, etc. But if you still have the legs left, I suggest you cross Tower Bridge and walk the Thames Path on the south side back to the Tate Modern, then cross the pedestrian Millennium Bridge to St. Paul’s, and THEN catch the #15 to Trafalgar Square for an above-ground ride through the City of London and lots of historic and brand new buildings.
This is what I call a nice day in London. We do large segments of this on every London visit. We love that city.