The signage for the Sainsburys' car park is rediculous. And, even if you know that there is a car park located behind Sainsburys, it is difficult to find.
I haven't noticed any new signs and use Google streetview to demonstrate my point, but the images are from 2016, so please photograph new signs that have been put up since.
Entering FH from the Horniman, you need to turn left here (see photo below), but there is no indication of the presence of a car park at the requisite left turn, and there has not even been signage for the car park beforehand.
If you are going out of Forest Hill (and probably not looking for a car park) then there is a very small sign, see below.
However, if you are luck enough to turn into Waldenshaw Road, at the end you will see a further sign when you reach the T-junction at its end, below, middle of image.
You correctly identify the right hand turn and proceed down Manor Mount until you get to the point shown in the below image where you need to turn right, but there is no sign. Carrying straight on leads you down a one-way road back to the S Circular.