In this paper, a framework is proposed for integration of peer-to-peer (P2P) trading-based local energy market (LEM) with the blockchain technology. The proposed LEM model allows prosumers and consumers to trade electricity among each other ensuring the presence of the retailer and network utility – who are also essential parts of a P2P network. The P2P contracts settled between various prosumers and consumers are governed by mutually agreed upon smart contracts – which are then written in an Ethereum blockchain to record and store bidding history, P2P transactions, and settlements. An effective formulation is also presented to capture P2P trading quantities and prices among participating prosumers and consumers in a decentralised fashion with an appropriate analysis of financial viability. Finally, a case study is conducted in a real Australian context; in which the engagement of both prosumers and consumers are taken into account, and the performance of the proposed blockchain-enabled LEM is compared with business-as-usual (BAU) to demonstrate the model's superiority.