To succeed in compensation claims for radiogenic injuries induced by their participation in the United Kingdom's atomic and nuclear weapons tests of the 1950s and 1960s, the 22,000 nuclear test veterans will have to satisfy Hill's Principles of Causation. Although they are blocked by legal restraints from suing the Crown, the evidential case for the veterans has been strengthening in recent years to a point where it would probably succeed in a UK court of law. The delay in mounting such a case has worked in favour of the veterans; if the legal constraints are removed, their chances of success are greater than if they had gone into court a decade ago. The article examines the evidence in support of their claims in relation to each of Hill's Principles.