This paper considers the stability of a financial system in which banks may interact through a lending market. We analyse a discrete time model in which households and banks are located on a circular city. Households present banks with risky investment opportunities which banks fund through deposits and interbank borrowing. In the event of bankruptcy a bank defaults on its interbank loans potentially resulting in contagion and losses for other banks. Through simulation we examine the susceptible of the financial system to systemic events, demonstrating the non-linear relationship between market concentration, shock severity and bankruptcies. The role and effect of regulatory actions such as loan insurance, minimum bank capitalisation and constraints on the size of borrowing relationships, are considered in limiting these effects.