Why do people appear less friendly and more rushed in large cities like London and New York vis-a-vis smaller countryside towns?

Axiom:
The opportunity cost (the potential value you are missing out on) of people in larger cities is much greater than the opportunity cost of those living in smaller country towns.

Example:
Asking for directions on a busy street or in a busy train station may result in you being ignored or brushed off. Do the same in a small town and people are likely to take their time to help you out.

Because London has a higher wage rate and a wide array of activities to partake in, stopping to chat or stopping to help others has a larger opportunity cost than it might have for those in a less activity rich town.