Hi there and thank you for your question,
I will try to assist you with your legal question but please feel free to ask as many follow up questions as you like until you are 100% satisfied.
No, strictly speaking a foreigner does NOT require a work permit in order to secure a rental of a property in South Africa. BUT, the landlord / rental agent might have some reservations about how you're going to pay the monthly rental (especially if the lease is a 12 month lease - and not just a 1 month holiday let) and the landlord will then want some "comfort" as to how you are going to finance the rental. e.g. do you have money in SA, or are you going to work here and pay rent from your salary. If it is the later, then they might want to see your work permit to ensure that you are legally allowed to work here. Basically, the landlord is covering his/her bases to ensure that you won't pay rent for 1 month and then just "squat" in the house for the next 6 months - rent free, and then fly back to the UK leaving the landlord with no way to recover his/her damages.
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Good luck and best regards,