Iceland confirmed that its Welling store on 53 Bellegrove Road would be closing on Saturday (February 1).
The reason behind the closure was not disclosed.
Since its announcement, Iceland says its colleagues have been offered jobs in other stores.
One customer, who wishes to remain anonymous, said the store had handed out £5 vouchers ahead of the closure.
An Iceland spokesperson said: “We can confirm our Welling Iceland store is scheduled to close on 1st February.
“Our store colleagues have entered into a consultation process and have been offered opportunities at surrounding stores where possible.”