The increasing demand for learning English as a second language has led to a growing interest in methods for automatically assessing spoken language proficiency. Most approaches use hand-crafted features, but their efficacy relies on their particular underlying assumptions and they risk discarding potentially salient information about proficiency. Other approaches rely on transcriptions produced by ASR systems which may not provide a faithful rendition of a learner's utterance in specific scenarios (e.g., non-native children's spontaneous speech). Furthermore, transcriptions do not yield any information about relevant aspects such as intonation, rhythm or prosody. In this paper, we investigate the use of wav2vec 2.0 for assessing overall and individual aspects of proficiency on two small datasets, one of which is publicly available. We find that this approach significantly outperforms the BERT-based baseline system trained on ASR and manual transcriptions used for comparison.