In this paper, we investigate the use of block quantisers based on Gaussian mixture models (GMMs) for the coding of Mel frequency-warped cepstral coefficient (MFCC) features in distributed speech recognition (DSR) applications. Specifically, we consider the multi-frame scheme, where temporal correlation across MFCC frames is exploited by the Karhunen-Loeve transform of the block quantiser. Compared with vector quantisers, the GMM-based block quantiser has relatively low computational and memory requirements which are independent of bitrate. More importantly, it is bitrate scalable, which means that the bitrate can be adjusted without the need for re-training. Static parameters such as the GMM and transform matrices are stored at the encoder and decoder and bit allocations are calculated "on-the-fly" without intensive processing. We have evaluated the quantisation scheme on the Aurora-2 database in a DSR framework. We show that jointly quantising more frames and using more mixture components in the GMM leads to higher recognition performance. The multi-frame GMM-based block quantiser achieves a word error rate (WER) of 2.5% at 800 bps, which is less than 1% degradation from the baseline (unquantised) word recognition accuracy, and graceful degradation down to a WER of 7% at 300 bps.