In message , at 06:17:35 on
Sun, 3 Aug 2014, Charles Ellson remarked:
Can you use your Oyster card for Pay-as-You-Go from London Bridge to
Tundbridge Wells?

Not according to anything I can see on the NR website (assuming it is
up to date). There doesn't seem to be anything definite announced
since e.g. "A spokesman for Southeastern confirmed: “We’re in
discussions with Transport for London to extend Oyster into Dartford."
[Kent Online 21 Feb 2014]

Tunbridge Wells being even further away from Greater London and AFAIAA
with a lower thicko count (Dartford seems to have a particular problem
with people unaware that Oyster has geographical limits) might not be
so far up the list for providing Oyster.

The problem with extending Oyster is that it has a very finite number of
price-zones and it's possible these were exhausted when extended to
Shenfield.
--
Roland Perry