BML2 is further up the queue than Chelt to Kingham, but it's got a flaw. The big problem with BML2 is that it doesn't serve the West End and City.
Changing at Canary Wharf/Stratford to Crossrail/Jubilee/Central line doesn't cut it - those lines are/will be full.
What's needed in South London is either a Crossrail style tunnel to take stoppers off the main lines, giving a 4 fast tracks to London, or a set of express tunnels from London Bridge to Purley.
Of course, that's DECADES away as Crossrail 2 is next (and it's debatable if we can afford it at the same time as HS2▸ !)
Here's a good analogy:
Were we to create space for more trains at the coastal end of the line now, we would just be pouring more water into a blocked sink
Network Rail Spokesman