Background: Magnetic resonance imaging (MRI) of the brain could be a key diagnostic and research tool for understanding the neuropsychiatric complications of COVID-19. For maximum impact, multi-modal MRI protocols will be needed to measure the effects of SARS-CoV2 infection on the brain by diverse potentially pathogenic mechanisms, and with high reliability across multiple sites and scanner manufacturers. Methods: A multi-modal brain MRI protocol comprising sequences for T1-weighted MRI, T2-FLAIR, diffusion MRI (dMRI), resting-state functional MRI (fMRI), susceptibility-weighted imaging (swMRI) and arterial spin labelling (ASL) was defined in close approximation to prior UK Biobank (UKB) and C-MORE protocols for Siemens 3T systems. We iteratively defined a comparable set of sequences for General Electric (GE) 3T systems. To assess multi-site feasibility and between-site variability of this protocol, N=8 healthy participants were each scanned at 4 UK sites: 3 using Siemens PRISMA scanners (Cambridge, Liverpool, Oxford) and 1 using a GE scanner (Kings College London). Over 2,000 Imaging Derived Phenotypes (IDPs) measuring both data quality and regional image properties of interest were automatically estimated by customised UKB image processing pipelines. Components of variance and intra-class correlations were estimated for each IDP by linear mixed effects models and benchmarked by comparison to repeated measurements of the same IDPs from UKB participants. Results: Intra-class correlations for many IDPs indicated good-to-excellent between-site reliability. First considering only data from the Siemens sites, between-site reliability generally matched the high levels of test-retest reliability of the same IDPs estimated in repeated, within-site, within-subject scans from UK Biobank. Inclusion of the GE site resulted in good-to-excellent reliability for many IDPs, but there were significant between-site differences in mean and scaling, and reduced ICCs, for some classes of IDP, especially T1 contrast and some dMRI-derived measures. We also identified high reliability of quantitative susceptibility mapping (QSM) IDPs derived from swMRI images, multi-network ICA-based IDPs from resting-state fMRI, and olfactory bulb structure IDPs from T1, T2-FLAIR and dMRI data. Conclusion: These results give confidence that large, multi-site MRI datasets can be collected reliably at different sites across the diverse range of MRI modalities and IDPs that could be mechanistically informative in COVID brain research. We discuss limitations of the study and strategies for further harmonization of data collected from sites using scanners supplied by different manufacturers. These protocols have already been adopted for MRI assessments of post-COVID patients in the UK as part of the COVID-CNS consortium.