Thanks Toni. However, it's not unknown for records to be missing from the national lists at GRO, I've had it happen before. I suppose I ought to contact Birmingham Records Office to see if it's in their lists.
The Horsfall name may be a red herrring I suppose, especially as it must have been from the memory of one of his relatives, him being dead by the time his son married, but then it's a distinctive name.
I've also tried a few searches in Ancestry with a wildcard, eg Kim*. I often try searches without a surname, but that's difficult with such popular forenames and with little else to distinguish the individuals.