I am looking for garage space within the Sydenham or Forest Hill area to rent to park up my motorcycle. I won't be needing access everyday but want to get to it when I need it.

I'm afraid I can't directly help, but I have just seen a similar request (not this area) on the 'London Bikers' facebook site.
My husband and I once responded to a gumtree ad when we lived in West Hampstead for someone looking to share a rented garage - it worked really well for a few years, before we moved here.
So maybe try those sites if you haven't already.