A well functioning interbank market is essential for efficient financial intermediation. But interbank exposures imply the possibility of direct contagion: the insolvency of a single institution may trigger multiple bank failures due to direct credit exposures. The complete network of interbank exposures that gives rise to this channel of contagion is not observable, making it difficult to assess the systemic risk it poses. This paper uses data on loans and deposits between UK-resident banks to estimate the distribution of bilateral exposures. The potential for contagion is examined by assuming the sudden failure of each individual bank and estimating the losses incurred to other banks as a result of the initial shock. This study suggests that, while a single bank failure is rarely sufficient to trigger the outright failure of other banks, it does have the potential to weaken substantially the capital holdings of the banking system. And, when the failure of a single bank does result in knock-on effects, their severity depends greatly on the maintained assumptions about the distribution of interbank loans and the level of loss given default. But data constraints mean that drawing definitive conclusions is difficult.