We develop a transductive meta-learning method that uses unlabelled instances to improve few-shot image classification performance. Our approach combines a regularized Mahalanobis-distance-based soft k-means clustering procedure with a modified state of the art neural adaptive feature extractor to achieve improved test-time classification accuracy using unlabelled data. We evaluate our method on transductive few-shot learning tasks, in which the goal is to jointly predict labels for query (test) examples given a set of support (training) examples. We achieve state of the art performance on the Meta-Dataset, mini-ImageNet and tiered-ImageNet benchmarks. All trained models and code have been made publicly available at github.com/plai-group/simple-cnaps.