Beth, if you look at the TripAdvisor link in Harleydonski's post, it explains the way to get 2-4-1 offers. As Acraven says, you need a paper Travelcard from a rail station (not an Oyster card, and not a paper Travelcard from a tube station).
Note that the London Pass only gets you "skip the line" entry at six sights, and the Churchill War Rooms are not one of these six. Because of the movie The Darkest Hour, these are now very popular. I got there with no pass or advance ticket at about 9:45 AM, thinking I'd beat the crowds. Well, others had the same idea, and I waited 20-30 minutes to get in. By the time I got in, there was a very large line behind me - many wearing their London Pass on the lanyard, waiting with everyone else. Those with prebooked time tickets had only a short wait.
I was in London twice this year - April 2019 and September 2019. I didn't get a London Pass either time, but I learned some useful tricks:
1) Do look at the London Pass list of covered attractions. Through this, I learned about the Museum of Brands, Packaging, and Advertising, and the London Jewish Museum. Both were very worthwhile. You may discover a non-famous place that draws you.
2) MANY sights now have a discount for advance online booking, of £1-5 per ticket. So, before I left for my second trip, I registered at the various websites of places I was interested in, but didn't actually buy any advance tickets because I wasn't sure of my itinerary. When I decided one morning to go to Greenwich that day, it was easy to book tickets on my phone since I had pre-registered, and I saved £5.25 this way. Some tickets can be scanned off the phone, while others cannot (you need to use the email to get a ticket at the window). Annoyingly, many websites don't specify. I was able to have my hotel print out my Greenwich tickets, but it turned out they could have scanned the PDF off my phone.