The Covid-19 mortality rate varies between countries and over time but the extent to which this is explained by the underlying risk in those infected is unclear. Using data on all adults in England with a positive Covid-19 test between 1st October 2020 and 30th April 2021 linked to clinical records, we examined trends and risk factors for hospital admission and mortality. Of 2,311,282 people included in the study, 164,046 (7.1%) were admitted and 53,156 (2.3%) died within 28 days of a positive Covid-19 test. We found significant variation in the case hospitalisation and mortality risk over time, which remained after accounting for the underlying risk of those infected. Older age groups, males, those resident in areas of greater socioeconomic deprivation, and those with obesity had higher odds of admission and death. People with severe mental illness and learning disability had the highest odds of admission and death. Our findings highlight both the role of external factors in Covid-19 admission and mortality risk and the need for more proactive care in the most vulnerable groups.