There has been significant recent interest in local electricity trading platforms, and particularly in the application of distributed ledger and blockchain technology for distributed, or peer-to-peer energy trading in local energy communit- ies. Several projects worldwide have demonstrated this concept on a small scale in Low Voltage (LV) distribution networks and microgrids. However, previous work in this area has not sufficiently addressed the potential impacts of peer-to-peer energy trading and other local electricity trading mechanisms on the control, operation and planning of the electricity distribution networks. Accordingly, this paper presents a methodology for the co-simulation of power distribution networks and local peer-to-peer energy trading platforms. The distribution system simulator is inter- faced with a peer-to-peer energy trading platform, which employs a blockchain-based distributed double auction trade mechanism. The presented co-simulation approach is demonstrated using a case study of typical European suburban distribution network. It is demonstrated in the paper that this approach can be used to analyse the impacts of peer-to- peer energy trading on network operational performance. The analysis presented in the paper suggests that a moderate level of peer-to-peer trading does not have significant impacts on network operational performance.