Immunisation remains the most cost-effective mechanism to combat global influenza infection and is widely employed against seasonal influenza viruses. Zoonotic transmission of avian influenza A viruses represents a significant threat to human health given the lack of population level immunity, which could translate into an influenza pandemic. Therefore, there is a need to better understand pre-existing human immunity against avian influenza strains. as highlighted by the recent rapid, global spread of avian H5Nx clade 2.3.4.4b variants. Here, we sought to quantify the frequencies and specificities of B cells recognising avian hemagglutinin (HA) within unexposed adults, and to characterise the ability of seasonal immunisation to boost cross-reactive immune responses to H5Nx strains, including from clade 2.3.4.4b. Low but detectable serum antibody titres against H5 and H7 avian influenza HA were observed in donors. The frequency of memory B cells with cross-reactive recognition of H5 and H7 HA was low and 2-5 fold lower than populations of seasonal H1N1 and H3N2 HA-specific B cells. Boosting of B cell responses against H5Nx clade 2.3.4.4b HA following seasonal immunisation were sporadic with only 3 out of 19 individuals showing an increased population of probe-positive cells. Cross-reactive B cells generally expressed immunoglobulins drawn from variable heavy chain genes associated with recognition of the HA stem (VH6-1, VH1-69, VH1-18). CD4+ T cell responses towards H5 HA were also weakly boosted with little to no increase in circulating T follicular helper cell populations. These findings highlight the need for avian influenza-specific vaccine products to bolster immunity in human populations, with consideration for use in pre-pandemic preparedness to expand baseline frequencies of avian influenza-specific memory B and T lymphocytes.