While block transform image coding has not been very popular lately in the presence of current state-of-the-art wavelet-based coders, the Gaussian mixture model (GMM)-based block quantiser, without the use of entropy coding, is still very competitive in the class of fixed rate transform coders. In this paper, a GMM-based block quantiser of low computational complexity is presented which is based on the discrete cosine transform (DCT). It is observed that the assumption of Gaussian mixture components in a GMM having Gauss-Markov properties is a reasonable one with the DCT approaching the optimality of the Karhunen-Lo/`eve transform (KLT) as a decorrelator. Performance gains of 6 to 7 dB are reported over the traditional single Gaussian block quantiser at 1 bit per pixel. The DCT possesses two advantages over the KLT: being fixed and source independent, which means it only needs to be applied once; and the availability of fast and efficient implementations. These advantages, together with bitrate scalability, result in a block quantiser that is considerably faster and less complex while the novelty of using a GMM to model the source probability density function is still preserved.