Are you sure there are no larger cities without a TV studio? I'm not sure all of the larger European countries have regional or local TV.
There are twenty cities in the EU with one million inhabitants or more (at least according to Wikipedia
). If you exclude the capital cities (who, one assumes, must all have fully fledged TV studios), that leaves Hamburg, Barcelona, Munich, Milan, Cologne, Birmingham and Naples. I know there are full service TV studios in most major German cities (at least those where an ARD member is headquartered), and they have at least one in Barcelona. Don't know about Milan or Naples, though.
It depends on what you term as a TV studio or even a 'full service TV studio' - what sort of size and facilities and of course it depends on what factor you determine as the size of a city
I think that Birmingham's problem is also it's strength - it's in the middle of the country. If the BBC and the single ITV want a centre to serve the 'North' then Manchester is the obvious place but Birmingham is too near to both London and Manchester to warrant having big studio centres in all 3.