The Doctor Who story 'The Web of Fear' of 1968 was indeed set on the
Underground, although the BBC were quoted such a ridiculous price to
film on the actual Underground and with so many understandable strings
attached that they built their own set of a short platform which could
be redressed to represent a number of stations and a couple of sections
of tunnel (one straight and one with a junction) which were apparently
so convincing that LT believed that a film crew had broken in and
filmed without permission. The only location filming was done in the
Woolwich foot tunnel. The one surviving episode can be seen on the
'Lost in Time' DVD release and while the Underground sets are very
detailed the junction appears several times in odd places (such as
while the characters are walking from Covent Garden to Goodge Street).

The Quatermass to which you refer is the Hammer film of 'Quatermass and
the Pit' and the underground station was all in studio as far as I'm
aware.