The within-host evolution of influenza is a vital component of its epidemiology. A question of particular interest is the role that selection plays in shaping the viral population over the course of a single infection. We here describe a method to measure selection acting upon the influenza virus within an individual host, based upon time-resolved genome sequence data from an infection. Analysing sequence data from a transmission study conducted in pigs, describing part of the haemagglutinin gene (HA1) of an influenza virus, we find signatures of non-neutrality in six of a total of sixteen infections. We find evidence for both positive and negative selection acting upon specific alleles, while in three cases, the data suggest the presence of time-dependent selection. In one infection we observe what is potentially a specific immune response against the virus; a non-synonymous mutation in an epitope region of the virus is found to be under initially positive, then strongly negative selection. Crucially, given the lack of homologous recombination in influenza, our method accounts for linkage disequilibrium between nucleotides at different positions in the haemagglutinin gene, allowing for the analysis of populations in which multiple mutations are present at any given time. Our approach offers a new insight into the dynamics of influenza infection, providing a detailed characterisation of the forces that underlie viral evolution.