Sorry, I misread the situation. I was looking at Sidcup-Dartford rather than Sidcup-Greenwich.
In that case, Sidcup is related to Dartford, Hither Green and Slade Green.
http://www.atoc.org/clientfiles/File/routeing_point_identifier.pdf page 56
Greenwich is related to Charlton and the London Group.
http://www.atoc.org/clientfiles/File/routeing_point_identifier.pdf page 27
We now need to find out which routeing points are appropriate by comparing single fares.
Sidcup-Greenwich
SDS £2.80 (not London)
SDS £4.80 (London not Underground)
Dartford-Greenwich
SDS £4.90 > £4.80 hence Dartford is not an appropriate routeing point.
Hither Green-Greenwich
SDS £1.80 (not London)
SDS £3.40 (London not Underground)
Both less than the Sidcup fares, so Hither Green is an appropriate routeing point.
Slade Green-Greenwich
SDS £3.30 (not London)
Greater than the equivalent Sidcup fare, so Slade Green is not an appropriate routeing point.
Therefore, the only appropriate routeing point for Sidcup is Hither Green.
Sidcup-Charlton
SDS £2.80, equal to the Greenwich fare so Charlton is an appropriate routeing point.
Sidcup-London
SDS £4.80, equal to the appropriate Greenwich fare so London is an appropriate routeing point.
Hither Green-Charlton allows map NK, giving us:
Sidcup-Hither Green-Lewisham-Charlton-Greenwich
Sidcup-Hither Green-New Cross-Lewisham-Charlton-Greenwich
Sidcup-Hither Green-Lewisham-Dartford-Charlton-Greenwich
Sidcup-Hither Green-New Cross-Lewisham-Dartford-Charlton-Greenwich
http://www.atoc.org/clientfiles/File/maps.pdf page 79
Hither Green-London allows map SV, giving us:
Sidcup-Hither Green-New Cross-London-Greenwich
http://www.atoc.org/clientfiles/File/maps.pdf page 100
So, I believe that you can use a Sidcup-Greenwich ticket to travel via Dartford, so long as you purhcase the route 'not London' ticket and make the Sidcup-Dartford leg via Hither Green and Lewisham.