Nosocomial transmission of SARS-CoV-2 has the potential to place a large burden on the healthcare system through, for example, increased patient length of stay, pressure on specialist care capacity and staff shortages. In England, a number of interventions were applied in hospitals over wave 1 of the COVID-19 pandemic to limit the spread of SARS-CoV-2 among both hospital inpatients and healthcare workers (HCWs). Using a computational modelling approach, we have estimated the combined effect of these, and other changes within the hospital setting, to determine how many nosocomial infections were averted. While highly uncertain, due primarily to important gaps in the evidence base, model results suggest that in a scenario with high occupancy, no testing, reduced infection prevention and control (IPC) measures, increased visitors, and longer patient stays, approximately 5.2% (3.9-7.2%) of all susceptible inpatients (n=140,603; 95% CI, 89,352-197,977 patients in total), and 51.1% (43.6, 55.3%) of patient-facing HCWs could have been nosocomially infected with SARS-CoV-2 over wave 1 compared with the 1.0% (0.7, 1.2%) of patients (33,922; 24,089- 41,015) and 20.3% (15.8-29.4%) of HCW observed to be nosocomially infected. The most effective interventions for prevention of nosocomial infections in patients were decreasing occupancy, increasing spacing between beds, and testing patients on admission, resulting in a reduction of 23,434 (14,544, 31,341), 10,979 (2,458, 16,979), and 9,505, (4588, 12,823) infections, respectively. Although every intervention had some impact, it was the collective impact of all interventions that demonstrated greatest effect, averting 140,603 (89,352, 197,977) infections in inpatients. In HCWs, the most effective intervention was universal mask use, with inclusion of universal masking as part of IPC measures averting 46.0% (42.9-54.5%) of infections in HCWs resulting in 17,980 (2,772-28,450) fewer infections per 100,000 patient-facing HCWs. Interventions introduced over wave 1 of the SARS-CoV-2 pandemic in England reduced HCW infection rates by 51.1% (43.6-55.3%).