Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) variants of concern (VOCs) now arise in the context of heterogeneous human connectivity and population immunity. Through a large-scale phylodynamic analysis of 115,622 Omicron BA.1 genomes, we identified >6,000 introductions of the antigenically distinct VOC into England and analyzed their local transmission and dispersal history. We find that six of the eight largest English Omicron lineages were already transmitting when Omicron was first reported in southern Africa (22 November 2021). Multiple datasets show that importation of Omicron continued despite subsequent restrictions on travel from southern Africa as a result of export from well-connected secondary locations. Initiation and dispersal of Omicron transmission lineages in England was a two-stage process that can be explained by models of the country's human geography and hierarchical travel network. Our results enable a comparison of the processes that drive the invasion of Omicron and other VOCs across multiple spatial scales.