That may have been the case when the boundaries were more clear, however I've lived in SE22 almost all my life and that row of shops along FH road has been called by my family as Honor Oak. It then becomes Peckham Rye as you reach the park although the streets that are in SE22 that come off Forest Hill Road and Peckham Rye are East Dulwich.

For Wood Vale itself, I'd consider it to be Honor Oak as far as Langton Rise, then Forest Hill for the rest of it. With the streets on the Southwark side being in Dulwich.