SARS-CoV-2 adaptation to its human host is evidenced by the emergence of new viral lineages with distinct genotypic and phenotypic characteristics, termed variants of concern (VOCs). Particular VOCs have become sequentially dominant globally (Alpha, Delta, Omicron) with each evolving independently from the ancestral Wuhan strain. Omicron is notable for its large number of Spike mutations found to promote immune escape and re-infection. Most recently, Omicron BA.4 and BA.5 subvariants have emerged with increasing levels of adaptive immune escape threatening vaccine effectiveness and increasing hospitalisations. Here, we demonstrate that the most recent Omicron variants have enhanced capacity to antagonise or evade human innate immune defenses. We find Omicron BA.4 and BA.5 replication is associated with reduced activation of epithelial innate immune responses versus earlier BA.1 and BA.2 subvariants. We also find enhanced expression of innate immune antagonist proteins Orf6 and N, similar to Alpha, suggesting common pathways of human adaptation and linking VOC dominance to improved innate immune evasion. We conclude that Omicron BA.4 and BA.5 have combined evolution of antibody escape with enhanced antagonism of human innate immunity to improve transmission and possibly reduce immune protection from severe disease.