Ah, all is now clear! Forget about Coulsdon, or even Old Coulsdon. Now you've told us his name I've looked at the electoral roll for Reginald Prout and can see that The Parade in question is actually in Hooley. It's some distance south of Coulsdon even though it's technically in the parish.
The post code is CR5 3EE and the shops in question aren't known as The Parade any more but are numbered into Brighton Road itself. 5 The Parade appears to be the shop that is now the Handmade Period Door Co. and is numbered 60 Brighton Road. I've found a photo of The Parade in 1937 that I've attached as well as a modern shot of the shops and you can see the shop with the prominent SALE sign over the window.
Peter
