Was taught in UK schools in the 80s. The city was a grubby but sterile environment with the usual tropes of bloody sports and I think high tech policing: then, through a big old fence was the country, very gentrified country piles, but the gent who takes our hero in has I think been lobotomised for being too passionate and thus we learn that aside from the wealth, amenities, health care, education, space and general comfort, the rich have it just as tough (!)
This must surely be "The Guardians" a short novel by John Christopher, published in 1970. The protagonist is a boy living in the "Conurb", a highly built-up but somewhat dystopian environment. It is surround by a high fence, separating it from the "Country". He succeeds in crossing the fence, and making his way to the rural environment. At first it appears to be far more pleasant, but he discovers that it is ruled by an equally totalitarian regime. One method to exert control is to operate on the brains of troublemakers, to remove their rebellious tendencies, akin to a lobotomization. He encounters a number of people with eccentric hobbies (clock-making, bonsai) who have been treated in this way.