While sharing files in a peer-to-peer (P2P) system significantly increases both the speed of retrieving the contents and the robustness of the system, tracing the access of files is not straightforward, even in the case of private P2P networks. In fact, a participant that has uploaded a file to a P2P network is not necessarily involved in its download. Additionally, due to the nature of the P2P network it is possible for a participant to already have all the fragments of a file, even before requesting it. This work tries to address the problem of tracing file access in a private P2P file sharing network through the use of blockchains to improve quality of service and auditability. To this end, the proposed solution combines three elements: (1) A distributed hash table network that is used to distribute encrypted files with redundancy amongst the partner peers; (2) Shamir's secret sharing scheme to split the secret keys of each file; (3) A blockchain network to distribute and manage the secret shares amongst the partner peers. In fact, the latter makes access to a file undeniable to every node of the network. The solution is relevant for consortia that manage a shared data pool on base of P2P technology with unrestricted access to files but where access to a file has to be recorded due to legal or billing reasons.