John Rowland:
Something else worth considering is that a crossover cavern has to
have more than twice the radius of the running tunnels, and four times
the cross-sectional area.

Well, that's true if the crossover is placed in a cylindrical cavern
and the two through tracks are straight and, immediately beyond the
cavern, in separate single-track tunnels. If making a crossover cavern
that size is a major problem, other geometries are possible. For
example, trains of moderate speed can have tracks spaced close enough
to use a single twin-track tunnel smaller than twice the diameter of
a single-track tunnel, and crossovers can fit within this.

Another option is step-plate junctions at each end of the crossover.
Another option is non-cylindrical tunnels, with stronger lining as needed.

Another thing worth mentioning is that most of the UndergrounD was
deliberately built beneath public highways in order to avoid wayleave
payments to landowners.

Indeed, in the early days it wasn't even legal to tunnel under someone
else's private property; you had to buy it outright. My impression from
what I've read is that this changed between 1890 and about 1900, but
I don't know exactly when.
--
Mark Brader "Could you please continue the petty bickering?
Toronto I find it most intriguing."
-- Data ("Haven", ST:TNG, Tracy Torme)

My text in this article is in the public domain.