My experience with this has definitely been related to geography. I grew up on the US West Coast in California. There, it is considered downright rude to acknowledge people by look or glance and especially not verbally if you are just passing in the street. Town, country makes no difference, people there seem easily offended by any violation of the "unwritten rules".
We moved to the Houston area several years ago (the epitome of "The South" with all the "southern hospitality" connotations that are ascribed to it) and it is almost the opposite here. Normal (N/T type) people are flabbergasted, shocked and saddened when I relate what is considered "acceptable social behavior" for casual passers-by on the street on the West Coast. Here, they don't feel like you're friendly unless you at least smile and nod, it's not necessary to talk. People are very welcoming and friendly here.
I always felt persecuted in California, because I was always somehow violating the unwritten rules and committing crimes of unforgivable weirdness. But here I feel confident that people will smile at me and yet not expect me to play the "how's the weather" game in conversation. It's enough to feel seen and liked from a safe distance and I really love that.
I lived in the central California area for over 10 years and only made a couple friends. I have lived in Houston for only a couple of years, have met many likable people and have more friends now than at any other time in my life. They are mostly not particularly close friends (although there are a couple good potentials) and they come and go, but it is a nice change from the isolation. People are more open to just being friendly here than they were in California and that has had a significant impact on my ability to socialize.
I have heard from other people who have been to the Eastern US coast say that folks are similar to California there as well. Ignoring people, eyes averted, rushing everywhere, acting hostile if acknowledged in any way. My theory, FWIW, is that there are greater financial pressures on the two US coastal areas due to higher costs of living, real estate, higher pressure lifestyles and so on. So, possibly it is related to anxiety and stress. Certainly California is a stressful place to live and work despite all it's great PR as a vacation spot.
In my experience, the places where greater eye contact and social familiarity seem to be more acceptable seem to be in the more rural and country areas where there is physical space and the pace of life is a bit slower. Heck, when we went to Oklahoma, the people there actually talked slower. Physically talked slower. It creeped our California real estate agent out on the phone lol! She thought she'd talked to a somewhat mentally impaired person at first. We assured her "no they really all talk that slow out there." They were also some of the friendliest, most considerate and politest people I've ever met.
So, perhaps you might find in the UK that out in the country and rural areas people may have the time for more nods and smiles whereas on the Underground and about London, for example, they keep their eyes glued to the map overhead to avoid accidentally impinging on another's already crowded personal space.