The aim of this work is to explore the connection between variability in single pulse intensity and periodic switching of the position angle (PA) of the linear polarisation and how this relates to the radio emission mechanism. There are five pulsars reported in the literature for which the PA is seen to periodically change in tandem with the variability in their pulse shapes. This behaviour is seemingly incompatible with two well established models of the radio emission mechanism. The purpose of this study is to investigate in a systematic way whether this phenomenon is common or if only happens in special cases, using a high-quality sample of pulsar data observed with the Parkes telescope. We show that the connection between polarisation variability and intensity variability is more common than previously expected.