We use a double-calibrated general equilibrium model to decompose the growth of the high-skilled wage premium in the UK from 1979 to 2000 into a range of potential contributory factors. This structural approach ensures that the model used is consistent with both price and quantity data simultaneously, and allows us to investigate a wide range of plausible parameter values. We find that the small observed rise in the skill premium is the net outcome of a set of opposing effects, some of which are large. In particular, the negative effect on the skill premium from the rising supply of skilled labour is mostly offset by the factor bias of technical change in favour of skilled labour. To this extent our work supports previous labour-market based studies, but is novel in showing that these are consistent with trade price and volume changes in a general equilibrium framework. If we assume a production technology dominated by capital-skill complementarity, the fall in capital prices (positive effect on the skill premium) and the sector bias of technical change in favour of unskilled-labour-intensive sectors (negative effect) also become quantitatively important. The impact of international trade and consumer preferences on the skill premium is mostly positive, and while not large compared to the role of factor bias, it is still significant as a proportion of to the net change in the wage premium. We conclude that a structural model such as ours provides robust insights into the processes that drive the skill premium. At the same time, while we treat the rise in the supply of skilled labour as exogenous, future research might usefully aim to endogenize skill acquisition decisions and labour market policies with a more fully dynamic modelling technique.