Diseases which are transmitted by the bites of insects can be spread to new locations through the movement of both infected insects and infected hosts. The importance of these routes has implications for disease control, because we can often restrict host movement, and so potentially reduce spread, but cannot easily restrict insect movements. Despite this, the importance of host movements has been little studied. Here we develop a mathematical model which allows us to disentangle and quantify transmission by insect dispersal and by host movement. We apply the model to two diseases of cattle and sheep transmitted by biting midges that have emerged in northern Europe in the past decade, bluetongue virus (BTV) and Schmallenberg virus (SBV). For both viruses, we show insect movements account for a majority of spread between farms. Although they cannot sustain an epidemic on their own, animal movements play an important role in introducing disease to new areas.