Estimates of volcanic source mass flux, currently deduced from observations of plume height, are crucial for ash dispersion models for aviation and population hazard. This study addresses the role of the atmospheric wind in determining the height at which volcanic plumes spread in the atmosphere and the relationship between source mass flux and plume height in a wind field. We present a predictive model of volcanic plumes that describes the bending over of the plume trajectory in a crosswind and show that model predictions are in accord with a dataset of historic eruptions if the profile of atmospheric wind shear is described. The wind restricts the rise height of volcanic plumes such that obtaining equivalent rise heights for a plume in a windy environment would require an order of magnitude increase in the source mass flux over a plume in a quiescent environment. Our model calculations are used to calibrate a semi-empirical relationship between the plume height and the source mass flux that explicitly includes the atmospheric wind speed. We demonstrate that the model can account for the variations in plume height observed during the first explosive phase of the 2010 Eyjafjallajökull eruption using independently measured wind speeds and show that changes in the observed plume height are better explained by changing meteorology than abrupt changes in the source mass flux. This study shows that unless the wind is properly accounted for, estimates of the source mass flux during an explosive eruption are likely to be very significant underpredictions of the volcanic source conditions.