Peer-to-peer energy-trading platforms (P2P) have the potential to transform the current energy system. However, research is presently scarce on how people would like to participate in, and what would they expect to gain from, such platforms. We address this gap by exploring these questions in the context of the UK energy market. Using a qualitative interview study, we examine how 45 people with an interest in renewable energy understand P2P. We find that the prospective users value the collective benefits of P2P, and understand participation as a mechanism to support social, ecological and economic benefits for communities and larger groups. Drawing on the findings from the interview analysis, we explore broad design characteristics that a prospective P2P energy trading platform should provide to meet the expectations and concerns voiced by our study participants.