Seasonal influenza has considerable impact around the world, both economically and in mortality among risk groups. The long term patterns of disease are hard to capture with simple models, while the interplay of epidemiological processes with antigenic evolution makes detailed modelling difficult and computationally intensive. We identify a number of characteristic features of flu incidence time series in temperate regions, including ranges of annual attack rates and outbreak durations. We construct pseudo-likelihoods to capture these characteristic features and examine the ability of a collection of simple models to reproduce them under seasonal variation in transmission. Results indicate that an age-structured model with non-random mixing and co-circulating strains are both required to match time series data. The extent of matching behaviour also serves to define informative ranges for parameters governing essential dynamics. Our work gives estimates of the seasonal peak basic reproduction, R0, in the range 1.7-2.1, with the degree of seasonal variation having limited impact of these estimates. We find that it is only really possible to estimate a lower bound on the degree of seasonal variation in influenza transmissibility, namely that transmissibility in the low transmission season may be only 5-10% less than the peak value. These results give some insight into the extent to which transmissibility of the H1N1pdm pandemic virus may increase in Northern Hemisphere temperate countries in winter 2009. We find that the timescale for waning of immunity to current circulating seasonal influenza strain is between 4 and 8 years, consistent with studies of the antigenic variation of influenza, and that inter-subtype cross-immunity is restricted to low levels.