Critical Covid-19 is caused by immune-mediated inflammatory lung injury. Host genetic variation influences the development of illness requiring critical care1 or hospitalisation2-4 following SARS-CoV-2 infection. The GenOMICC (Genetics of Mortality in Critical Care) study enables the comparison of genomes from critically-ill cases with population controls in order to find underlying disease mechanisms. Here, we use whole genome sequencing in 7,491 critically-ill cases compared with 48,400 controls to discover and replicate 23 independent variants that significantly predispose to critical Covid-19. We identify 16 new independent associations, including variants within genes involved in interferon signalling (IL10RB, PLSCR1), leucocyte differentiation (BCL11A), and blood type antigen secretor status (FUT2). Using transcriptome-wide association and colocalisation to infer the effect of gene expression on disease severity, we find evidence implicating multiple genes, including reduced expression of a membrane flippase (ATP11A), and increased mucin expression (MUC1), in critical disease. Mendelian randomisation provides evidence in support of causal roles for myeloid cell adhesion molecules (SELE, ICAM5, CD209) and coagulation factor F8, all of which are potentially druggable targets. Our results are broadly consistent with a multi-component model of Covid-19 pathophysiology, in which at least two distinct mechanisms can predispose to life-threatening disease: failure to control viral replication, or an enhanced tendency towards pulmonary inflammation and intravascular coagulation. We show that comparison between critically-ill cases and population controls is highly efficient for detection of therapeutically-relevant mechanisms of disease.