Wheat yields in organic production are significantly lower than those achieved in conventional farming systems and in Northern Europe organic farmers also struggle to achieve the processing quality levels demanded by millers and bakers, especially in winter-wheat crops. Here, we report the findings of a 3-year pilot study which investigated the potential of increasing grain yields and both standard processing (e.g., grain protein levels and specific weights) and selected nutritional (tocopherol and tocotrienol isomers) quality parameters via (i) changes in the management of clover crops grown before wheat (Rhizobium seed inoculation, application of greenwaste compost to clover swards) and (ii) use of new varieties developed in both the UK and continental Europe. Results indicate that the use of compost amendment to preceding clover swards significantly increased the grain protein levels in the three winter-wheat, but not the four spring-wheat varieties, and also significantly increases grain yields in one winter-wheat variety (Greina). In contrast, the use of Rhizobium-inoculation was found to significantly reduce protein concentrations in the winter-, but not spring wheat varieties, and had no significant effect on grain yields in both winter and spring wheat. However, analysis of variance detected significant interactions between Rhizobium seed inocula in clover pre-crops and (a) compost application for grain specific weights in winter-wheat and grain hardness in spring wheat crops and (b) variety for grain protein content in spring wheat crops. No significant effect of clover pre-crop management on tocopherol and tocotrienol isomer profiles could be detected, although significant differences between varieties were detected in both winter and spring wheat. Results of this pilot study need to be confirmed in future trials, but indicate that both (a) changes in clover-management practices and (b) the selections of wheat varieties that are more suitable for organic farming systems has the potential to increase grain yield and allow organic farmers to more frequently achieve baking or milling grade quality.