The workers demanded to be allowed to speak with the owner.

Literal

Workers [topic-は] owner [with-と] talk [object-を] let-do [imperative-させろ] [quotative-と] demanded.

話をさせろ combines causative させる with the plain imperative ~ろ: 'let us talk!' The と packages this as the content of the demand. The workers' frustration comes through in the blunt imperative form.