The discovery of three individuals suspected to have contracted variant Creutzfeldt-Jakob disease (vCJD) through blood transfusions has heightened concerns that a secondary epidemic via human-to-human transmission could occur in the UK. The Department of Health responded immediately to this threat by banning those who had received blood transfusions since 1980 from donating blood. In this paper, we conduct a sensitivity analysis to explore the potential size of a blood-borne vCJD epidemic and investigate the effectiveness of public health interventions. A mathematical model was developed together with an expression for the basic reproduction number (R0). The sensitivity of model predictions to unknown parameters determining the transmission of vCJD via infected blood was assessed under pessimistic modelling assumptions. We found that the size of the epidemic (up until 2080) was bounded above by 900 cases, with self-sustaining epidemics (R0>1) also possible; but the scenarios under which such epidemics could arise were found to be biologically implausible. Under optimistic assumptions, public health interventions reduced the upper bound to 250 and further still when only biologically plausible scenarios were considered. Our results support the belief that scenarios leading to large or self-sustaining epidemics are possible but unlikely, and that public health interventions were effective.