http://www.oldmapsonline.org/en/Lewisham...&scale_to=
Lots of lovely maps here to research.

sydenham town forum has some threads on local roman roads,
but is not clear to me if anything interesting was ever dug up at Blythe Hill.
The romans stuck to the higher lands to keep a watch out for any potential ambush, so maybe.
wiki is convinced that the road ran down ivydale (the long straight bit obviously), past St. Hilda's Church, and up the hill, so it must be true....
https://en.wikipedia.org/wiki/London_to_Lewes_Way