I haven't phrased that correctly, I mean cities proper. Merseyside includes boroughs like Knowlsey which includes St Helens absolutely removed from Liverpool both physically and culturally (no surprise it voted leave). Liverpool (City), Wirral and Sefton, which are the main areas of urban Liverpool, voted Remain. Merseyside is not synonymous with Liverpool, likewise Greater Manchester includes yokel places like Wigan which are culturally and physically separate from Manchester.
Birmingham as a CITY voted Leave, which makes it different. You're comparing counties with cities there, maybe my mistake in saying 'metropolitan area's but counties aren't automatically that either. London is also totally different from any other area in the country, because Greater London can be classified as one city in a way which Greater Manchester or Merseyside simply cannot.