COVID-19 patients at risk of severe disease may be treated with neutralising monoclonal antibodies (mAbs). To minimise virus escape from neutralisation these are administered as combinations e.g. casirivimab+imdevimab or, for antibodies targeting relatively conserved regions, individually e.g. sotrovimab. Unprecedented genomic surveillance of SARS-CoV-2 in the UK has enabled a genome-first approach to detect emerging drug resistance in Delta and Omicron cases treated with casirivimab+imdevimab and sotrovimab respectively. Mutations occur within the antibody epitopes and for casirivimab+imdevimab multiple mutations are present on contiguous raw reads, simultaneously affecting both components. Using surface plasmon resonance and pseudoviral neutralisation assays we demonstrate these mutations reduce or completely abrogate antibody affinity and neutralising activity, suggesting they are driven by immune evasion. In addition, we show that some mutations also reduce the neutralising activity of vaccine-induced serum.