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 SARS-CoV-2 in high biocontainment laboratories. We evaluated the ability of IgG and IgM ELISAs targeting SARS-CoV-2 spike subunit 1 receptor binding domain (S1-RBD), and spike subunit 2 (S2) and nucleocapsid protein (NP), at predicting the presence and magnitude of NAb determined by PRNT. IgG S2 + NP ELISA was 96.8% [95% CI 83.8–99.9] sensitive and 88.9% [95% CI 51.8–99.7] specific at predicting the presence of NAbs (PRNT80 > 1:40). IgG and IgM S1-RBD ELISAs correlated with PRNT titre, with higher ELISA results increasing the likelihood of a robust neutralising response. The IgM S1-RBD assay can be used as a rapid, high throughput test to approximate the magnitude of NAb titre.