The concept of the peer-to-peer local energy market (P2P LEM) is no longer novel to the energy community. Yet, its large-scale implementation within the current electricity network remains a complex challenge. One key reason is the lack of understanding of the supplier licensing models in different countries. For instance, in the UK, up to year 2023, a consumer is only allowed to have a single supplier at a time under its single licence supplier model. This directly contradicts the existing P2P trading models that allow a consumer to purchase electricity from multiple sellers within the local market. Given this context, this article conducts a review of recent literature and government policies in different countries on the P2P LEM and identifies the barriers behind the lack of large-scale P2P trading implementation in today’s electricity markets. We explain how these barriers can be overcome by engaging prosumers in traditional and private distribution networks through either licensed or license-exempt suppliers. Particularly, we discuss six P2P LEM frameworks that can be utilised to address the supplier licensing issue. Finally, this review presents a summary of risks, and recommendations to aid the regulatory framework to implement P2P LEM.