Have you flown to Europe before? Some people can function their first day upon landing, but most of us find the first day is a jet-lagged haze. Fine for walking around, but not good for anything requiring concentration or lots of time indoors. Some of us are tired the next day as well. You definitely don't want to plan anything on the arrival day that requires pre-payment, in case you arrive late and miss it, or arrive on time and just don't feel up to it. And even if you feel OK during they day, you are most likely to be tired early, so whatever you do, don't plan on theatre your first night, or it will just be an expensive nap!
I also agree that with "3.5" days in London (I'm not sure exactly how you're calculating that), you can see a some of London, or can see even less of London and one side trip. You also don't want to exhaust yourself before your tour starts, as the tour will be busy.
The London Pass is only a good value if you are seeing a lot of the covered attractions. It's hard to make it pay off unless you're running around a lot, and as I said, even if that's your intention, you may not be up to it. Many things in London are free. Those that aren't usually have a discount for online booking (you can do this the morning you go for most things). And if you want to see the Churchill War Rooms, these now have long lines due to the movie The Darkest Hour. While admission to them is included in the London Pass, you don't get skip the line privledges. For them, it's best to pre-book a ticket online with an admission time.
What day and time do you arrive in London? I assume you're taking the Eurostar to Paris - what day and time is the departure? Remember that it's recommended to get to St. Pancras station an hour before the departure, to go through the formalities. And, what are your absolute priorities for London and surrounding daytrips? With this information, we can help you plan a good few days in London, that won't leave you needing a rest before the start of your 14 day BOE tour.