Spinal magnetic resonance (MR) scans are a vital tool for diagnosing the cause of back pain for many diseases and conditions. However, interpreting clinically useful information from these scans can be challenging, time-consuming and hard to reproduce across different radiologists. In this paper, we alleviate these problems by introducing a multi-stage automated pipeline for analysing spinal MR scans. This pipeline first detects and labels vertebral bodies across several commonly used sequences (e.g. T1w, T2w and STIR) and fields of view (e.g. lumbar, cervical, whole spine). Using these detections it then performs automated diagnosis for several spinal disorders, including intervertebral disc degenerative changes in T1w and T2w lumbar scans, and spinal metastases, cord compression and vertebral fractures. To achieve this, we propose a new method of vertebrae detection and labelling, using vector fields to group together detected vertebral landmarks and a language-modelling inspired beam search to determine the corresponding levels of the detections. We also employ a new transformer-based architecture to perform radiological grading which incorporates context from multiple vertebrae and sequences, as a real radiologist would. The performance of each stage of the pipeline is tested in isolation on several clinical datasets, each consisting of 66 to 421 scans. The outputs are compared to manual annotations of expert radiologists, demonstrating accurate vertebrae detection across a range of scan parameters. Similarly, the model’s grading predictions for various types of disc degeneration and detection of spinal metastases closely match those of an expert radiologist. To aid future research, our code and trained models are made publicly available.