Three years ago we “blitzed” London over a three-day period and the London Pass was (barely) worth the expense financially. The biggest value to the card was the ability to skip the ticket queues and head right to the entrance.
This year, on a seven day trip, we are forgoing the London Pass because we want to focus on museums. The few venues which charge for admission we plan to visit just don’t add up to the expense of a multi-day London Pass.
If you plan on visiting a lot of the historic sites, you might want to research the English Heritage Society. Members receive free and/or discounted entrance in Heritage Trust properties as well as discounts elsewhere. An annual membership might be worth the cost depending on how many of their properties you plan to visit.
Good luck on your trip.