The development of large-scale facial identification systems that provide privacy protection of the enrolled subjects represents an open challenge. In the context of privacy protection, several template protection schemes have been proposed in the past. However, these schemes appear to be unsuitable for indexing (workload reduction) in biometric identification systems. More precisely, they have been utilised in identification systems performing exhaustive searches, thereby leading to degradations of the computational efficiency. In this work, we propose a privacypreserving face identification system which utilises a Product Quantisation-based hash look-up table for indexing and retrieval of protected face templates. These face templates are protected through fully homomorphic encryption schemes, thereby guaranteeing high privacy protection of the enrolled subjects. For the best configuration, the experimental evaluation carried out over closed-set and open-set settings shows the feasibility of the proposed technique for the use in large-scale facial identification systems: a workload reduction down to 0.1% of a baseline approach performing an exhaustive search is achieved together with a low pre-selection error rate of less than 1%. In terms of biometric performance, a False Negative Identification Rate (FNIR) in range of 0.0% -0.2% is obtained for practical False Positive Identification Rate (FPIR) values on the FEI and FERET face databases. In addition, our proposal shows competitive performance on unconstrained databases, e.g., the LFW face database. To the best of the authors' knowledge, this is the first work presenting a competitive privacy-preserving workload reduction scheme which performs template comparisons in the encrypted domain.