However, I've just done a search on trains from New Cross to Lewisham (2
stations down the line and you should be able to easily switch to a
Sidcup service and there are 4 trains at least between 6pm and 7pm - at
6.02, 6.11, 6,20 and 6.50. After the 6.50 one, they change to roughly a
train every 30 minutes or so.

I think I see where I have gone wrong; I was relying on the SE Trains
timetable from their own website, which lists all the trains on the various
lines heading out towards Dartford. On that there is a gap in trians to New
Cross and beyond between 1823 and 1945. TfL's Journey planner came up with
simple changes at New Cross at 1823 and 1950 but all manner of convoluted
routes taking up to an hour and a half from Rotherhithe to Sidcup in between
these times, hence I went directlt to SE Trains themselves to check the
actual rail timetable.

However it appears Hayes trains also stop there which are not listed on the
same timetable.

My fault, and thanks for the information which saves a trip to London
Bridge- though still, it is very odd that they go from 4 an hour on the
Dartford lines all day, then there's a 1hr20 gap, then back up to 4 an hour
till 12.30am!