SARS-CoV-2 has caused a global outbreak of severe respiratory disease (COVID-19), leading to an unprecedented public health crisis. To date, there has been over thirty-three million diagnosed infections, and over one million deaths. No vaccine or targeted therapeutics are currently available. We previously identified a human monoclonal antibody, 47D11, capable of cross-neutralising SARS-CoV-2 and the related 2002/2003 SARS-CoV in vitro, and preventing SARS-CoV-2 induced pneumonia in a hamster model. Here we present the structural basis of its neutralization mechanism. We describe cryo-EM structures of trimeric SARS-CoV and SARS-CoV-2 spike ectodomains in complex with the 47D11 Fab. These data reveal that 47D11 binds specifically to the closed conformation of the receptor binding domain, distal to the ACE2 binding site. The CDRL3 stabilises the N343 glycan in an upright conformation, exposing a conserved and mutationally constrained hydrophobic pocket, into which the CDRH3 loop inserts two aromatic residues. Interestingly, 47D11 preferentially selects for the partially open conformation of the SARS-CoV-2 spike, suggesting that it could be used effectively in combination with other antibodies that target the exposed receptor-binding motif. Taken together, these results expose a cryptic site of vulnerability on the SARS-CoV-2 RBD and provide a structural roadmap for the development of 47D11 as a prophylactic or post-exposure therapy for COVID-19.