I'm traveling next month with 3 people who have not been to London. Well, my brother went in 1976 and my SIL's sis went in about the same time frame, lol. Both say they don't remember a thing so it's like 3 newbies.
What I'm doing with them is getting some walking in the first 2 days as this is how I do a new city on my own.
Arrival day - We'll walk from our hotel to Green Park (want to show my brother the RAF Bomber Command Memorial), then work our way around in front of Buckingham Palace and then thru St James's Park and back to the hotel. This gets us out in the sunshine (hope for sun!), green spaces, some flowers and some London scenery.
Full day 1 - We'll walk back to Wellington Barracks area to see the Changing of the Guard form up, then on to the Horse Guards and Trafalgar Square. We'll do the National Gallery this afternoon, then if folks still have energy will walk them to either Covent Garden or Piccadilly Square and ride the Tube back.
I'm not big on bus tours altho I have done them. The first time we went to Rome I booked a VIP airport pick up and tour that included an hour's worth of sightseeing. I mistakenly thought that would help us get oriented. It did not, mostly because of the crazy one way streets making it seem like we were driving in circles (which we probably were, hahah). It was extremely difficult to find our way back to some of the sights that looked interesting.
I do better studying a paper map, looking at where the walking tours go (either Rick's free ones or other suggestions online) and then heading out on foot. For myself this give me a better feel for the location.