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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. 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. 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. 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 [ABSTRACT FROM AUTHOR]