Convolutional neural networks (CNN) can accurately predict chronological age in healthy individuals from structural MRI brain scans. Potentially, these models could be applied during routine clinical examinations to detect deviations from healthy ageing, including early-stage neurodegeneration. This could have important implications for patient care, drug development, and optimising MRI data collection. However, existing brain-age models are typically optimised for scans which are not part of routine examinations (e.g., volumetric T1-weighted scans), generalise poorly (e.g., to data from different scanner vendors and hospitals etc.), or rely on computationally expensive pre-processing steps which limit real-time clinical utility. Here, we sought to develop a brain-age framework suitable for use during routine clinical head MRI examinations. Using a deep learning-based neuroradiology report classifier, we generated a dataset of 23,302 'radiologically normal for age' head MRI examinations from two large UK hospitals for model training and testing (age range = 18-95 years), and demonstrate fast (< 5 seconds), accurate (mean absolute error [MAE] < 4 years) age prediction from clinical-grade, minimally processed axial T2-weighted and axial diffusion-weighted scans, with generalisability between hospitals and scanner vendors (Δ MAE < 1 year). The clinical relevance of these brain-age predictions was tested using 228 patients whose MRIs were reported independently by neuroradiologists as showing atrophy 'excessive for age'. These patients had systematically higher brain-predicted age than chronological age (mean predicted age difference = +5.89 years, 'radiologically normal for age' mean predicted age difference = +0.05 years, p < 0.0001). Our brain-age framework demonstrates feasibility for use as a screening tool during routine hospital examinations to automatically detect older-appearing brains in real-time, with relevance for clinical decision-making and optimising patient pathways.