Such a system does not exist in exactly this form in the UK.
There are "Job agencies", "Employment agencies" and "Temping agencies". These either find workers to fill particular jobs (in return for a "finders fee") or will act as an employer for temporary staff. So if a company needs aan office worker, they can get a "temp" from the "temping agency". The company pays the agency and the agency pays the worker.
In teaching such agencies are known as "supply agencies", and in medicine they are called "Locum agencies" (a locum is a doctor working on a temporary contract).
So you could say
I was employed as a temporary office worker through a job agency 'Name of Agency'.
The alternative is to translate literally
I was a member of the Belgrade Youth Cooperative and worked through the cooperative as a temporary packer at a food factory.
By using capitals I show that this is "the thing named the Belgrade Youth Cooperative" and so warning the reader that the words might have a specific meaning.