This paper presents three innovative deep learning models for English accent classification: Multi-DenseNet, PSA-DenseNet, and MPSE-DenseNet, that combine multi-task learning and the PSA module attention mechanism with DenseNet. We applied these models to data collected from six dialects of English across native English speaking regions (Britain, the United States, Scotland) and nonnative English speaking regions (China, Germany, India). Our experimental results show a significant improvement in classification accuracy, particularly with MPSA-DenseNet, which outperforms all other models, including DenseNet and EPSA models previously used for accent identification. Our findings indicate that MPSA-DenseNet is a highly promising model for accurately identifying English accents.