Whilst all rail stations are connected by the tube, a cross London journey requires changing on the tube and perhaps changing the tube line once or twice, probably not the optimum solution. So what would we design if we were tasked with designing a city transport infrastructure today?
I think I would have all trains coming into one fairly inner ring and going round most if not all of the ring. Or other services that come into the city, round half of the ring and out of the other side. Obviously the ring would need to be several tracks wide to accomodate all the trains, but there would be no need for a dedicated ring service, as so many trains would be traveling the ring.
I have produced a rather basic diagram below to illustrate the point (on the left is a terminus system, on the right is a ring system):