Using a novel interpretation of dynamic networks, we analyse the network of livestock movements in Great Britain in order to determine the risk of a large epidemic of foot-and-mouth disease (FMD). This network is exceptionally well characterized, as there are legal requirements that the date, source, destination and number of animals be recorded and held on central databases. We identify a percolation threshold in the structure of the livestock network, indicating that, while there is little possibility of a national epidemic of FMD in winter when the catastrophic 2001 epidemic began, there remains a risk in late summer or early autumn. These predictions are corroborated by a non-parametric simulation in which the movements of livestock in 2003 and 2004 are replayed as they occurred. Despite the risk, we show that the network displays small-world properties which can be exploited to target surveillance and control and drastically reduce this risk.