All the major cities in the UK are short of rail capacity from the edge of the conurbation to the centre, and need more station capacity at what the Germans call a Hauptbahnhof to provide a central transport interchange.
To see the difference, consider Cologne Hbf, which has six tracks to the East and eight tracks to the northwest, giving a total connectivity score of 14. Berlin Hbf has 4 north, 4 south, 4 east, 4 west for a score of 16. I'm counting tracks beyond any station throat, before lines start to diverge away from the station.
The major cities in Britain by contrast score as follows:
- Birmingham New St: 4 East; 4 West: Score = 8
- Manchester Piccadilly: 2 West; 2 East; 4 South. Score = 8.
- Leeds: 6 West; 2 East. Score = 8
- Sheffield: 2 North; 2 South. Score = 4
- Bristol: 3 South; 2 East; 4 North. Score = 9
Sheffield needs four tracks south to Dore junction and four north to Nunnery junction, thus doubling its connection score to 8.
Birmingham New St is the closest we have to a Hauptbahnhof, but it is now too small. I'd propose to use New St as a dedicated commuter station, and add more platforms and tracks to the Curzon St/Moor St complex (connectivity score = 7) to turn it into a proper Hauptbahnhof for long-distance traffic, able to service 400m length trains on the WCML via Stetchford and via Handsacre, and with connections to the cross county routes via Water Orton and via Camp Hill.
Leeds is at the northern edge of the West Yorkshire conurbation, the northen end of the Birmingham-Leeds corridor and the Eastern end of the Liverpool-Leeds corridor. So it needs bay platforms on the south side of the station with access to the south, west and east. I'd build the proposed HS2 station as a south-facing "T", with 6 or more bay platforms and four tracks to the south, following the route of HS2 East, with chords to access Manchester via Wakefield Westgate; a chord to access Doncaster and the ECML at New Crofton; and a chord to access the northbound HS2 towards York.
Manchester needs more connectivity at a single station, which I suggest should be Piccadilly. With HS2, its connectivity will rise to 10, which is not enough. Adding an NPR tunnel towards Marsden will only make 12.
Instead of NPR, I'd build an underground line in Manchester on an East-West alignment, like Thameslink, with a four-platform station below ground at Piccadilly. To the north-west, the tunnel would connect onto the Chat Moss line and the line to Preston. To the south east, I'd connect into a re-quadded line towards Guide Bridge, and to the Stockport line just beyond Slade Lane junction. This "Thameslink North" would be separate from HS2, would be cheaper than HS2 West, and could be built first. This would give a connectivity score, without HS2, of 12. With HS2 that becomes 14, which is about right for the main interchange for the whole of the north of England.
Castlefield would then be dedicated to a high-frequency local service, eventually targetting 16tph or more.