> Somehow US airports always seem to be surrounded by densely populated residential areas, even in the direction of the runways, while Euro airports don’t seem to have this problem

London Heathrow is entirely hemmed in by surrounding urban areas. Flights landing at Heathrow fly directly over central London (with great views of iconic buildings).

It is technically possible to extend the runways somewhat but actually doing so is a planning / political nightmare. Heathrow is located just inside the M25 (the main London orbital motorway) immediately adjacent to the junction of the M25 and the M4 (the busy motorway that goes West from London). So not only is Heathrow virtually impossible to expand, it's in an area known for its horrendous rush-hour traffic. It does have a railway connection to central London, but this is a partially underground line with multiple stops (every few minutes in practice). Journeys to Heathrow from most places in the UK can be horrendous.

Gatwick, London's second airport, is ~30 miles South of the city, and does have reasonably fast rail connections. Gatwick does have space for a new runway, but lots of factors have prevented this.