This largely depends on where you are in the US. I have moved a lot over the years, from dense city centers, to the dirt roads of rural America. Here are my experiences:

NYC would probably be the most comparable to your experience in London, but seeing as I haven't lived there, I can instead talk about Boston. When I lived inside the subway range in Boston (Somerville specifically), my experience matches up with yours. I was ~5 minutes from a supermarket and ~15 minutes from the subway/train stop by foot. I was even closer to a couple bus stops for lines that would take me to places like a mall, nearby universities, or the next subway line over (we don't have an equivalent of the Circle line).

I currently live in Boston suburbs (Metrowest for people that know the area) and can't really walk anywhere as my street and adjacent streets don't have sidewalks. I could try to walk on the street, but with the narrowness combined with the speed at which people drive through this neighborhood, it would not be fun. If I hop in the car, I am ~5 minutes from a strip mall with a supermarket, pharmacy, liquor store, etc. and ~10 minutes from the commuter rail train station that I use to commute to the city for work. If I want to head to a large shopping hub with a mall, then it is ~20 minutes away by car. There is a skeleton of a bus system in my area, but it would require traversing ~1.5 miles on streets without sidewalks to get to the nearest stop for me.

When I lived in a rural area (rural PA), things were very different. To get to the nearest supermarket (a WalMart), it took ~30 minutes worth of driving. If I wanted to go to the mall, it was closer to 60 minutes. I am sure there are even less dense areas than that in this country.