Automatic speech recognition (ASR) technologies have been significantly advanced in the past few decades. However, recognition of overlapped speech remains a highly challenging task to date. To this end, multi-channel microphone array data are widely used in current ASR systems. Motivated by the invariance of visual modality to acoustic signal corruption and the additional cues they provide to separate the target speaker from the interfering sound sources, this paper presents an audio-visual multi-channel based recognition system for overlapped speech. It benefits from a tight integration between a speech separation front-end and recognition back-end, both of which incorporate additional video input. A series of audio-visual multi-channel speech separation front-end components based on TF masking, Filter&Sum and mask-based MVDR neural channel integration approaches are developed. To reduce the error cost mismatch between the separation and recognition components, the entire system is jointly fine-tuned using a multi-task criterion interpolation of the scale-invariant signal to noise ratio (Si-SNR) with either the connectionist temporal classification (CTC), or lattice-free maximum mutual information (LF-MMI) loss function. Experiments suggest that: the proposed audio-visual multi-channel recognition system outperforms the baseline audio-only multi-channel ASR system by up to 8.04% (31.68% relative) and 22.86% (58.51% relative) absolute WER reduction on overlapped speech constructed using either simulation or replaying of the LRS2 dataset respectively. Consistent performance improvements are also obtained using the proposed audio-visual multi-channel recognition system when using occluded video input with the face region randomly covered up to 60%.