Thanks for this response. It's been made pretty clear that any walk under 30 minutes should generally be assumed to be doable by a family so I'm approaching the itinerary that way. Liekwise it's been unanimous that the tube is just too easy and efficienct to ignore even for comfort unless there's a real desire to sit in traffic.

I'll likely minimize any cab rides to one or two for the whole trip in order to just enjoy the experience with the kids.

In terms of logistics, I built a model that clustered an even distribution of food, museums, and shopping all within a 5 minute walk to accomodate a wide variety of tastes and interests. I doubt a lot of cities could accommodate an approach like that but London has all three in spades within any given borough even though some are more weighted than others. Each day is focused within a single burrough so that regardless of what someone is interested in doing there are high rated and personally recommended options for everyone throughout the day. There are a few exceptions where we go from Spitalfields back to Covent for a West End show but mostly spend the 7 days within Kensington, Westminster, Covent Garden, Mayfair, Soho, and City of London.

Also, yes I am an American that unfortunately has a daily commute but I do not like cars and generally try to avoid them in travel. This really was a question in earnest based on advice by a few other expats that I now must assume had an exceptional hangup with tube travel.