Peer-to-peer (P2P) energy trading is an emerging energy supply paradigm where customers with distributed energy resources (DERs) are allowed to directly trade and share electricity with each other. P2P energy trading can facilitate local power and energy balance, thus being a potential way to manage the rapidly increasing number of DERs in net zero transition. It is of great importance to explore P2P energy trading via public power networks, to which most DERs are connected. Despite the extensive research on P2P energy trading, there has been little large-scale commercial deployment in practice across the world. In this paper, the practical challenges of conducting P2P energy trading via public power networks are identified and presented, based on the analysis of a practical Local Virtual Private Networks (LVPNs) case in North Wales, UK. The ongoing efforts and emerging solutions to tackling the challenges are then summarized and critically reviewed. Finally, the way forward for facilitating P2P energy trading via public power networks is proposed.