Actually, you can find plenty of references from the New York Times
from 1901 and 1902 referring to the London Tube.

Go to Google News and search. I've provided a shortened link he
http://bit.ly/q566GY

This is just mentions of "London Tube" together - there's even more
with the words not appearing contiguous within the publication in
question, but that would also throw up too many false positives.

On the second and third page of the search results there are some very
interesting ones.

Seems a lot of the tube was run by Americans at the start of the
century. When Bob Kiley, and then Tim O'Toole, ran it in our much more
recent history, there was quite a bit of hoo-hah and jingoism
regarding these appointments in some of the press. Ironic when you
consider the tube's early history - looks as though there's always
been a close connection with the US and the London tube - as indeed
there has been viceversa with the British involvement with the early
American railroads.

Anyway, can anyone beat New York Times 1901 for the earliest reference
of the London Tube to describe the whole system?