That looks pretty much how I'd have drawn it, although I'm not sure about the London-Cambridge-Peterborough line. Is that worth building as its own HS link?
It relieves capacity on the ECML, GEML, the WAML and probably the MML (Nottingham and possibly Sheffield) all in one package.
It totally eliminates the need to ever worry about Welwyn VIaduct/Welwyn North.
The bridge/tunnel to Ireland is also a nice feature, but I'm not sure how feasible it is!
Myself I think it is one of the things we
have to have for political and social reasons even though the economic case is not the best.
On a more serious note though, I'd have all the London HS lines terminate in one station though. I'm not convinced that running different HS lines into Paddington, Euston, St. Pancras and Kings Cross is a good idea.
Well Euston, St Pancras and KGX are essentially the same station, or would be after all three are rebuilt for high speed use.
Paddington is troublesome but there is no more room at the Euston road stations.
I'd be in full support of that, if it's a direct HS link from Southampton into London. But then, living in Southampton, of course I'd be in favour of that!
Indeed, I was thinking about routing it to Weymouth via Brighton, but that would be a sharp curve.
The main problem with an eastern alignment would be where to put the London station - St Pancras is already used for Eurostar and Kings Cross is constrained by space unless you do a Euston-style expansion to the east.
Just demolish the warehouses to the north of the station and dig it out, as the canal is above the level of the station platforms you can put it on an aqueduct across the station throat (as it has significant tourist use).
You can easily fit enough platforms in since almost everything left in KGX will be InterCity anyway.
That then just leaves the issue of the Cambridge/Peterborough line, but if that is going into Kings Cross that isn't too much of a disaster in getting onto HS2, however it's a little harder to get to the HSSW. To overcome this it could be that both routes are one by means of a tunnel under London.
Essentially it would be the reconstructed King's Cross, with essentially no remaining classic trains (as the only thing left pretty much after the Thameslink Programme is the Intercity/Cambridge Cruisers).
Euston-St Pancras-Kings Cross are increasingly just becoming one interconnected station complex, along the lines of Gare du Nord and Gare de l'Est.
Paddington is a little further away but there is little that can be done there, but if OOC is indeed a stop on both lines (myself I would have sacrified an OOC stop in favour of a Heathrow stop since you can't really have both) then you could transfer.
Or you could use the HSXC connection from near Swindon to Birmingham (perhaps at unnel under birmingham with a station under Curzon Street or a simpler connection to an enlarged Birmingham International complex) means that you can get to destinations north of Birmingham quite easily without going through London.
It also cuts several hours from the Edinburgh-Southampton journey since you can run high speed all the way to about Reading.
The one possible problem with the layout suggested is that to have that much network it may well be that HS2 phase one would start to be running out of capacity, as such the question then is, would it be better to quad track to Birmingham or to extend from Peterborough to Nottingham (and give it it's own HS station) before linking bak in to HS Phase 2 (east)? As with the latter the services to Leeds, York and Newcastle (or at least some of them) could then run via Peterborough, whislt still retaining the Birmingham to Leeds, York and Newcastle from the services which come from the SW via Swindon.
You could, if you are really short for capacity, extend the line north from Peterborough, but I would favour running some trains via Swindon, since you still only loose ten minutes by doing that.
A High Speed line or lines to the South Coast shouldn't be needed (given the short distances), however a line which can take 400m long Duplex trains would be very useful given the numbers of passengers involved (whether or not that is a new line is another matter).
New Lines are almost certainly cheaper compared to gauge clearing, especially in the mass of track that is the South London suburban network.
EDIT:
Additional spurs could go into Liverpool from the North and on the GEML route to go all the way to Norwich.
75km from Peterborough to Toton sidings.
That would cost a couple of billion pounds and probably produce about six additional paths as you need approximately:
2tph Norwich
2tph King's Lynn
2tph Nottingham (conventional)
2tph Sheffield (conventional)
2tph Leeds (conventional)
2tph York (conventional)
1tph Lincoln
1tph Hull
Many of these trains have to be 400m long cleared to allow for commuter rush hour services.
I would think some sort of Eurostar/AGV cross would be best.