> That makes it sound as if they'd been automated right from 1907, which most definitely isn't the case
From 1907 onwards every newly built line was automated from opening (though indeed extensions or "new" lines made by splitting an existing line were sometimes manually driven).
Even that is a bit disingenuous when you consider the very minimal number of completely new lines that have been built since 1906 – basically only the Victoria line in 1968 and (depending on whether you only count real tube lines or not) the DLR in 1987.
(The Jubilee line in 1979 – which started out being manually driven – wouldn't count according to your criteria, because part of it was "made by splitting an existing line", and apart from being heavy rail, arguably Crossrail could be argued to be an extension, too, even though it does operate automatically on the new-built bits, i.e. the central section plus the Abbey Wood branch.)
From 1907 onwards every newly built line was automated from opening (though indeed extensions or "new" lines made by splitting an existing line were sometimes manually driven).