Key for Service Door - Anyone know about these for buildings from the 1950s

My friend has an inset service door in his bathroom. It is inset into a cavity which contains all the pipes to his bathroom for his apartment which was built in the 1940's/1950's. At the moment it is unlocked and doesn't close securely without locking and the draught makes using the bathroom freezing cold. He has asked the landlord for a key to lock it to no avail.

Anyone have an idea of what kind of key is needed and where he might be able to borrow one or purchase one cheaply?