Automatic identification and selective spraying of weeds (such as dock) in grass can provide very significant long-term ecological and cost benefits. Although machine vision (with interface to suitable automation) provides an effective means of achieving this, the associated challenges are formidable, due to the complexity of the images. This results from factors such as the percentage of dock in the image being low, the presence of other plants such as clover and changes in the level of illumination. Here, these challenges are addressed by the application of Convolutional Neural Networks (CNNs) to images containing grass and dock; and grass, dock and white clover. The performance of conventionally trained CNNs and those trained using 'Transfer Learning' was compared. This was done for increasingly small datasets, to assess the viability of each approach for projects where large amounts of training data are not available. Results show that CNNs provide considerable improvements over previous methods for classification of weeds in grass. While previous work has reported best accuracies of around 83%, here a conventionally-trained CNN attained 95.6% accuracy for the two-class dataset, with 94.9% for the three-class dataset (i.e. dock, clover and grass). Interestingly, use of Transfer learning, with as few as 50 samples per class, still provides accuracies of around 84%. This is very promising for agricultural businesses that, due to the high cost of collecting and processing large amounts of data, have not yet been able to employ Neural Network models. Therefore, the employment of CNNs, particularly when incorporating Transfer Learning, is a very powerful method for classification of weeds in grassland, and one that is worthy of further research.