Except that these jurisdictions (if they're simply talking about anything under 25,000) are very often suburbs that are within an hour's crowded drive of a metropolitan center. I grew up in a so-called village of 15,000 with express commuter trains to downtown Chicago.
I don't know how Britain figures this, but any large city in continental Europe I looked at had its official city limits out in the fields, whereas US cities have them well within a belt of "small towns". I remember a German gazetteer listing Chicago's population as 9 million, but the actual number of people living within Chicago is closer to 3 million. The difference being made up by just plain folks.
This is what Wikipedia says for Chicago -- the definition of urban is country specific:
- City 2,873,790(US: 3rd)
- Density 12,649/sq mi (4,816/km²)
- Urban 8,711,000
- Metro 9,785,747
-- Andy