Different vaccine strains included in the Live Attenuated Influenza Vaccine (LAIV) have variable efficacy. The reasons for this are not clear and may include differences in immunogenicity. We report a phase IV open‐label study on the immunogenicity of a single dose of quadrivalent LAIV (Fluenz™ Tetra) in children during the 2015/16 season, to investigate the antibody responses to different strains. Eligible children were enrolled to receive LAIV; nasal samples were collected before and approximately 4 weeks after immunisation. There was a significant increase in nasal IgA to the H3N2, B/Victoria lineage (B/Brisbane) and B/Yamagata lineage (B/Phuket) components, but not to the H1N1 component. The fold change in nasal IgA response was inversely proportional to the baseline nasal IgA titre for H1N1, H3N2 and B/Brisbane. We investigated possible associations that may explain baseline nasal IgA, including age and prior vaccination status, but found different patterns for different antigens, suggesting the response is multi‐factorial. Overall, we observed differences in immune responses to different viral strains included in the vaccine, the reasons for this require further investigation.