Yes save the money and use it elsewhere on your trip.
London is a walkable city.
A favorite suggestion of mine for first time visitors is to tube to Westminster Station ( Mind the Gap*), exit and walk out into Parliament Square.
After photo ops and and a tour of Westminster Abbey cross the street ( always wait for the lights cuz traffic flows in the opposite direction than your brain is wired for) and head to the well signed Birdcage Walk and stroll up to Buckingham Palace.
If the Churchill War Rooms are on your “ must see “ list (timed entry tickets only) they are off Birdcage Walk on Horseguard Road. So is the Horse Guard Parade Ground.
Right now use Google Maps overhead view to see what I’m talking about. You’ll see how easy it is to see the above.
Get your Oyster Card when you arrive. No need to get the Visitor’s Oyster before you go. Use your credit/debit card and get them from the kiosks when you arrive.
Lastly, Mind the Gap is a phrase you’ll hear and see when using the tube. Merely a reminder there might be a small space between the train and platform.
Great city. Enjoy yourselves!