Severe acute respiratory coronavirus 2 (SARS-CoV-2) has spread globally since its emergence in 2019. Most SARS-CoV-2 infections generate immune responses leading to rising levels of immunoglobulins (Ig) M, A and G which can be detected using diagnostic tests including enzyme-linked immunosorbent assays (ELISA). Whilst implying previous SARS-CoV-2 infection, the detection of Ig by ELISA does not guarantee the presence of neutralising antibodies (NAb) that can prevent the virus infecting cells. Plaque reduction neutralisation tests (PRNT) detect NAb but are not amenable to mass testing as they take several days and require use of viable SARS-CoV-2 in high biocontainment laboratories. We evaluated the ability of IgG and IgM ELISAs targeting SARS-CoV-2 spike subunit 1 (S1) and nucleocapsid protein (NP) at predicting the presence and magnitude of NAb determined by PRNT. SARS-CoV-2 IgG ELISA correlated well with NAb and was highly sensitive (93.8% [95% CI 79.2–99.2]) and specific (88.9% [95% CI 51.8–99.7%]) at predicting the presence of NAb. There was not a strong correlation between IgM ELISA and PRNT result. IgG ELISA provides a useful, high throughput method of predicting the presence of neutralising antibodies, with higher ELISA results increasing the likelihood of having a greater NAb titre.