The representation learning of speech, without textual resources, is an area of significant interest for many low resource speech applications. In this paper, we describe an approach to self-supervised representation learning from raw audio using a hidden unit clustering (HUC) framework. The input to the model consists of audio samples that are windowed and processed with 1-D convolutional layers. The learned "time-frequency" representations from the convolutional neural network (CNN) module are further processed with long short term memory (LSTM) layers which generate a contextual vector representation for every windowed segment. The HUC framework, allowing the categorization of the representations into a small number of phoneme-like units, is used to train the model for learning semantically rich speech representations. The targets consist of phoneme-like pseudo labels for each audio segment and these are generated with an iterative k-means algorithm. We explore techniques that improve the speaker invariance of the learned representations and illustrate the effectiveness of the proposed approach on two settings, i) completely unsupervised speech applications on the sub-tasks described as part of the ZeroSpeech 2021 challenge and ii) semi-supervised automatic speech recognition (ASR) applications on the TIMIT dataset and on the GramVaani challenge Hindi dataset. In these experiments, we achieve state-of-art results for various ZeroSpeech tasks. Further, on the ASR experiments, the HUC representations are shown to improve significantly over other established benchmarks based on Wav2vec, HuBERT and Best-RQ.