SE25 to Dulwich with the minimum amount of roads.
From the Dulwich College Roundabout to the park, you can cycle on the pavement - either past the picture gallery or along the south circular. This one uses the gallery way as it's quieter, the South Circular cyclepath can feel a bit dicey with small children - when the cycle route ends by the gallery, cross over to the other side of the road and continue on the gravel/dirt path up to the park gate.