Tom Anderson writes:
I have been told that the cost of making new tube tunnels depends on
their size ...

Well, sure. There's more mass to shift, and more surface to line.

I can see why it might be greater - there's more mass to shift, more
surface to line ...

There, see? :-)

A further issue is that in some cases only a small tube may be able
to fit into a narrow vertical or horizontal space between existing
obstacles -- either older tunnels or other underground structures, or
geological strata that you really don't want to have to tunnel through.
A large tunnel, if possible at all, would then incur special costs due
to moving the existing structures or tunneling through the difficult
terrain.

but not massively greater.

Typically that's true. I don't have numbers.

If it's only a bit more expensive, wouldn't it have made sense to
build the underground to be compatible with the rest of the network...?

Only if you think it's sensible for through services to be able to
operate between them using main line rolling stock, or for main line
rolling stock to be usable on the Underground even in the absence of
through services.

Historically, the subsurface lines (District, Hammersmith & City,
Metropolitan, etc.) *were* considered as an extension of the main-line
railway network, were built for compatibility with it, and were served
by through trains using main-line rolling stock.

But later management saw the inter-working as a source of problems and
found it preferable to treat these lines as a separate sort of thing;
main-line connections at Ealing Broadway, Kensington (Olympia),
Paddington, King's Cross, St. Pancras, Farringdon, Liverpool Street,
Shoreditch, New Cross, New Cross Gate, and other points I can't
remember offhand were all taken out of regular service, and in most
cases the connecting tracks were eventually lifted.

The tube lines, on the other hand, are descended ultimately from the
Tower Subway of 1870, the little cable-operated line whose tunnel
diameter was only about 6'8". When you compare a tunnel *that* size
to a tunnel of 16' or more to carry main-line stock, the incremental
costs don't look so small!

The promoters of the Tower Subway planned their second line to be
slightly larger, using 8' tubes; after the Tower Subway failed, they
suspended the proposal, then eventually upgraded it to the longer and
larger line that opened in 1890 as the City & South London Railway,
using a tube diameter of 10'2". This was still viewed as a self-
contained line for local traffic, so there was no strong reason for
compatibility. In fact, it was going to be cable-hauled until late
in the construction period.

It was found that the C&SLR trains were inconveniently small; the
next few tubes, opened from 1898 to 1907, mostly chose slightly
larger diameters and this gave rise to today's standard, while the
the C&SLR was enlarged to a compatible tunnel size at considerable
cost and inconvenience. But it wasn't until the suburban extensions
of the 1930s that people really started thinking of tube train routes
of the length that now exist, and by then the small size was pretty
much locked in.
--
Mark Brader "You have seen this incident, based on
Toronto sworn testimony. Can you prove that it
didn't happen?" -- Plan 9 from Outer Space

My text in this article is in the public domain.