Automatic speech recognition (ASR) of overlapped speech remains a highly challenging task to date. To this end, multi-channel microphone array data are widely used in state-of-the-art ASR systems. Motivated by the invariance of visual modality to acoustic signal corruption, this paper presents an audio-visual multi-channel overlapped speech recognition system featuring tightly integrated separation front-end and recognition back-end. A series of audio-visual multi-channel speech separation front-end components based on \textit{TF masking}, \textit{filter\&sum} and \textit{mask-based MVDR} beamforming approaches were developed. To reduce the error cost mismatch between the separation and recognition components, they were jointly fine-tuned using the connectionist temporal classification (CTC) loss function, or a multi-task criterion interpolation with scale-invariant signal to noise ratio (Si-SNR) error cost. Experiments suggest that the proposed multi-channel AVSR system outperforms the baseline audio-only ASR system by up to 6.81\% (26.83\% relative) and 22.22\% (56.87\% relative) absolute word error rate (WER) reduction on overlapped speech constructed using either simulation or replaying of the lipreading sentence 2 (LRS2) dataset respectively.