FWIW the oldest extant station in London is Deptford, opened in 1836, although to look at it you wouldn't realise since it's been rebuilt at least once. The old carriage ramp is still visible, though, and apparently there's a project in train (no pun intended!) to restore it. The viaducts that trains run along from London Bridge as far as Greenwich all date from the same period.
At the other end of the same line, the old platforms of Spa Road station, the original terminus of the London and Greenwich railway, can be seen from trains east of London Bridge station. That's got to be the oldest disused station in London.
The Spa Road you can still see is on a different site to the original Spa Road terminus of the London & Greenwich Railway (which was to the north), so I don't think Spa Road gets the prize either.
I'm going to have to think about this one...