Many healthcare facilities report SARS-CoV-2 outbreaks but transmission analysis is complicated by the high prevalence of infection and limited viral genetic diversity. The contribution of different vectors to nosocomial infection or the effectiveness of interventions is therefore currently unclear. Detailed epidemiological and viral nanopore sequence data were analysed from 574 consecutive patients with a PCR positive SARS-CoV-2 test between March 13th and March 31st, when the pandemic first impacted on a large, multisite healthcare institution in London. During this time the first major preventative interventions were introduced, including progressive community social distancing (CSD) policies leading to mandatory national lockdown, exclusion of hospital visitors, and introduction of universal surgical facemask-use by healthcare-workers (HCW). Incidence of nosocomial cases, community SARS-CoV-2 cases and infection in a cohort of 228 HCWs followed the same dynamic course, decreasing shortly after introduction of CSD measures and prior to the main hospital-based interventions. We investigated clusters involving nosocomial cases based on overlapping ward-stays during the 14-day incubation period and SARS-CoV-2 genome sequence similarity. Our method placed 63 (79%) of 80 sequenced probable and definite nosocomial cases into 14 clusters containing a median of 4 patients (min 2, max 19) No genetic support was found for the majority of epidemiological clusters (31/44, 70%) and genomics revealed multiple contemporaneous outbreaks within single epidemiological clusters. We included a measure of hospital enrichment compared to community cases to increase confidence in our clusters, which were 1-14 fold enriched. Applying genomics, we could provide a robust estimate of the incubation period for nosocomial transmission, with a median lower bound and upper bound of 6 and 9 days respectively. Six (43%) clusters spanned multiple wards, with evidence of cryptic transmission, and community-onset cases could not be identified in more than half the clusters, particularly on the elective hospital site, implicating HCW as vectors of transmission. Taken together these findings suggest that CSD had the dominant impact on reducing nosocomial transmission by reducing HCW infection.