The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) Omicron variant (B.1.1.529) rapidly replaced Delta (B.1.617.2) to become dominant in England. Our study assessed differences in transmission between Omicron and Delta using two independent data sources and methods. Omicron and Delta cases were identified through genomic sequencing, genotyping and S-gene target failure in England from 5-11 December 2021. Secondary attack rates for named contacts were calculated in household and non-household settings using contact tracing data, while household clustering was identified using national surveillance data. Logistic regression models were applied to control for factors associated with transmission for both methods. For contact tracing data, higher secondary attack rates for Omicron vs. Delta were identified in households (15.0% vs. 10.8%) and non-households (8.2% vs. 3.7%). For both variants, in household settings, onward transmission was reduced from cases and named contacts who had three doses of vaccine compared to two, but this effect was less pronounced for Omicron (adjusted risk ratio, aRR 0.78 and 0.88) than Delta (aRR 0.62 and 0.68). In non-household settings, a similar reduction was observed only in contacts who had three doses vs. two doses for both Delta (aRR 0.51) and Omicron (aRR 0.76). For national surveillance data, the risk of household clustering, was increased 3.5-fold for Omicron compared to Delta (aRR 3.54 (3.29-3.81)). Our study identified increased risk of onward transmission of Omicron, consistent with its successful global displacement of Delta. We identified a reduced effectiveness of vaccination in lowering risk of transmission, a likely contributor for the rapid propagation of Omicron.