Eliot bank, Canonbie Road and College Road are all roads I find very quiet. The four ways up sydenham hill to my recall aren't crazy busy and there's a bus lane in at least some of them. Gipsy Hill and Anerly Road are both busier than I'd like, but you might be fine with them, it depends on your comfort levels. I also seem to remember the roads around the Horniman having actual honest-to-god cycle lanes on them (but could have faulty memory)
Eliot bank, Canonbie Road and College Road are all roads I find very quiet. The four ways up sydenham hill to my recall aren't crazy busy and there's a bus lane in at least some of them. Gipsy Hill and Anerly Road are both busier than I'd like, but you might be fine with them, it depends on your comfort levels. I also seem to remember the roads around the Horniman having actual honest-to-god cycle lanes on them (but could have faulty memory)