There are premises on Kirkdale that might be suitable. As @Anotherjohn says, depending on the amount of cooking you’re doing you may need change of use approval from Lewisham Planning. But that shouldn’t be too hard and depends on whether you’re cooking on the premises. Eg a sandwich shop can trade from A1 retail premises, as long as they’re only reheating on the premises, not cooking from scratch. Fig & Pistachio cafe for example traded quite happily on A1 without change of use. And even if you do require change of use then on very small (below 150sqm) you don’t need full planning permission, just prior approval from the council.
This is a complicated way of saying don’t worry too much about the change of use process - it’s sortable and there’s plenty of advice available.
Saigon Cafe at 138 Kirkdale must have recently gone through (or are maybe still going through?) the change of use process, so maybe contact them for advice?
Saigon Cafe have the added complication that they are in a Grade II Listed building so they will need additional consents (something Waffle Station didn’t do for the huge exterior flue they installed).
But there are plenty of premises on Kirkdale that don’t have Listed building restrictions. And Kirkdale High Street is quite a foodie hub and that sort of clustering is good for trade.
Here are some possibilities …
The former Fig & Pistachio cafe premises at 101 Kirkdale. Lewisham has recently refused permission for a nail bar. I don’t think anyone objected to the change of use, but the owner had made a big mistake on the type of approval applied for. He may come back again with that one, but if the nail bar people have gone elsewhere then that premises might be suitable for you. Icy Cakes have just opened a few doors away and as they’re not cooking on the premises they didn’t need change of use.
On the corner of Fransfield Grove and Kirkdale is a former Thai restaurant that has been boarded up for 18 years! That is the perfect site for a restaurant or cafe/bar. It’s in a prominent location with a lot of passing trade and a big wide pavement for extra tables.
If that’s too big then there are three other vacant shops in that parade that might be suitable.