No spare rail capacity

Balcombe Viaduct in a 1954 photograph
The LAMBS website has a very interesting post on the (im)possibility of carrying more passengers on the London–Brighton line:

[Mayfield is] a completely unsustainable development from the transport perspective .. You have to remember that the Brighton mainline has only got four lines from London as far as Balcombe Tunnel, which is just South of Crawley. Beyond that it’s a two track railway going down to Brighton and I can see no way of actually widening that section of line. You’ve got a number of obstacles in your way which would have to be addressed because of the undulating way of the countryside.

Much more here.
Update 25th January: Lee Newlyn responds.