Genomic surveillance of SARS-CoV-2 has provided a critical evidence base for public health decisions throughout the pandemic. Sequencing data from clinical cases has helped to understand disease transmission and the spread of novel variants. Genomic wastewater surveillance can offer important, complementary information by providing frequency estimates of all variants circulating in a population without sampling biases. Here we show that genomic SARS-CoV-2 wastewater surveillance can detect fine-scale differences within urban centres, specifically within the city of Liverpool, UK, during the emergence of Alpha and Delta variants between November 2020 and June 2021. Furthermore, wastewater and clinical sequencing match well in the estimated timing of new variant rises and the first detection of a new variant in a given area may occur in either clinical or wastewater samples. The study's main limitation was sample quality when infection prevalence was low in spring 2021, resulting in a lower resolution of the rise of the Delta variant compared to the rise of the Alpha variant in the previous winter. The correspondence between wastewater and clinical variant frequencies demonstrates the reliability of wastewater surveillance. However, discrepancies in the first detection of the Alpha variant between the two approaches highlight that wastewater monitoring can also capture missing information, possibly resulting from asymptomatic cases or communities less engaged with testing programmes, as found by a simultaneous surge testing effort across the city.