There's several places on Sydenham High Street (one 3 minute stop on the train if you don't drive). It depends on what you want really. The halal butchers (Haji & son?) has some hard food/soup provisions, hardough bread and seasoning. Further down past Superdrugs, Istanbul minimart usually has most other things you would be looking for.

For a bigger range of shops (and hair products galore!) Peckham is the answer.