There is now intense interest in developing a new industrial policy for the UK which, among other aims, will encourage more UK-based firms to shift towards higher value added activities in a range of industries. In this paper we argue that, if any such industrial policy is to be effective in improving UK economic performance, it needs to stimulate higher levels of innovation by firms. In particular, the policy must encourage a sizeable number of firms who do not currently engage in innovation to start doing so. This in turn implies an increased demand for innovation-related skills and knowledge by UK firms that is unlikely to be met by an industrial training system which is beset by historical weaknesses. Thus the emergence of new industrial policy needs to be complemented by new training policies designed to make skills development and utilisation more cost-effective and to stimulate higher levels of employer demand for innovation-related skills and training. These new policies will need to be balanced in three dimensions: between technical and generic skills, between higher and intermediate skills, and between initial and continuing education and training.