We propose a single-channel Deep Cascade Fusion of Diarization and Separation (DCF-DS) framework for back-end automatic speech recognition (ASR), combining neural speaker diarization (NSD) and speech separation (SS). First, we sequentially integrate the NSD and SS modules within a joint training framework, enabling the separation module to leverage speaker time boundaries from the diarization module effectively. Then, to complement DCF-DS training, we introduce a window-level decoding scheme that allows the DCF-DS framework to handle the sparse data convergence instability (SDCI) problem. We also explore using an NSD system trained on real datasets to provide more accurate speaker boundaries. Additionally, we incorporate an optional multi-input multi-output speech enhancement module (MIMO-SE) within the DCF-DS framework, which offers further performance gains. Finally, we enhance diarization results by re-clustering DCF-DS outputs, improving ASR accuracy. By incorporating the DCF-DS method, we achieved first place in the realistic single-channel track of the CHiME-8 NOTSOFAR-1 challenge. We also perform the evaluation on the open LibriCSS dataset, achieving a new state-of-the-art single-channel speech recognition performance.