This is something that can be disputed for days on end. The size of a city can be measured in many way.
Population
Number of people employed
Number of businesses
The area the city covers
The list is endless.
Manchester and Birmingham have been flighting for the second slot for years, likewise Leeds vs Manchester or Liverpool for the third slot. If the Metro areas aren't included then Leeds is bigger than Manchester.
Here goes anyway.....
London
Birmingham
Leeds
Sheffield
Manchester
Include the Metro areas.....
London
Birmingham
Manchester
Leeds
Sheffield
rant over, back to pprune