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Purpose: Accurate surveillance of the COVID-19 pandemic can be weakened by under-reporting of cases, particularly due to asymptomatic or pre-symptomatic infections, resulting in bias. Quantification of SARS-CoV-2 RNA in wastewater (WW) can be used to infer infection prevalence, but uncertainty in sensitivity and considerable variability has meant that accurate measurement remains elusive. Methods & Materials: Data from 44 sewage sites in England, covering 31% of the population, are used in this analysis where samples are available from July 2020 to present day. Samples include the raw SARS-CoV-2 gene copy number and associated meta-data. To establish the sensitivity and specificity of the WW data, we compare to population representative prevalence surveys available across England (the ONS Covid Infection Survey - CIS). The WW data were mapped to sub-regional data of the CIS and fitted using mathematical modelling. First, a phenomenological model was developed to model how infected individuals shed SARS-CoV-2 into WW and how the markers may degrade in time and compare this to the data. Second, we develop a model to estimate SARS-CoV-2 prevalence directly from WW data which is trained on the CIS data. Results: Data from 44 sewage sites in England, shows that SARS-CoV-2 prevalence is estimated to within 1.1% of estimates from representative prevalence surveys (with 95% confidence). Using machine learning and phenomenological models, differences between sampled sites, particularly the WW flow rate, influence prevalence estimation and require careful interpretation. SARS-CoV-2 signals in WW appear 4-5 days earlier in comparison to clinical testing data but are coincident with prevalence surveys suggesting that WW surveillance can be a leading indicator for asymptomatic viral infections. Conclusion: Wastewater-based epidemiology complements and strengthens traditional surveillance, with significant implications for public health. Using WW to quantify infection prevalence requires knowledge of additional meta-data and outbreak detection needs to account for unexplained aberrations in WW data to improve reliability