Vaccines that trigger an influenza-specific cytotoxic T cell (CTL) response are a prime candidate for providing broadly efficacious protection against the transmission of novel influenza A viruses (IAV). The efficacy of T cell vaccines may vary between hosts depending on pre-existing influenza-specific T cells directed toward conserved epitopes of IAV and the existence of humoral immunity, making the population-level impact of vaccination campaigns against emerging pandemic viruses uncertain. We consider use of a hypothetical T cell vaccine in a moderately severe pandemic, assuming a background of heterogeneously distributed pre-existing cellular and strain-specific humoral immunity. We consider both the achievable reduction in the attack rate, and by adopting a simple model linking epidemic progression to the emergence of antigenic variants, the suppression of antigenic drift during the initial pandemic wave. We demonstrate that widespread administration of T cell vaccines t hat are efficacious in influenza-experienced hosts (adults) and influenza-naive hosts (children) can mitigate a moderate IAV pandemic, but that T cell vaccines may be an inefficient control measure if the pandemic IAV shares its ancestry with seasonal IAVs that circulated in previous decades or many hosts have naturally acquired CTL protection that is difficult to boost further. Unless T cell vaccines are significantly less efficacious in naive hosts, a limited stockpile of vaccines is best distributed to naive hosts due to their enhanced potential for transmission, regardless of the existence of humoral immunity amongst experienced hosts. We show that impact of CTL vaccination on antigenic drift may be modest if naturally induced CTL responses commonly regulate influenza infections. However if enhanced CTL responses enable rapid within-host viral clearance, T cell vaccines may significantly reduce within-host selection pressures that facilitate population-level strain turnover.