We present a study of observed Type II supernova (SN II) colours using optical/near-infrared photometric data from the Carnegie Supernovae Project-I. We analyse four colours (B−V, u−g, g−r, and g−Y) and find that SN II colour curves can be described by two linear regimes during the photospheric phase. The first (s1,colour) is steeper and has a median duration of ∼ 40 days. The second, shallower slope (s2,colour) lasts until the end of the “plateau” (∼ 80 days). The two slopes correlate in the sense that steeper initial colour curves also imply steeper colour curves at later phases. As suggested by recent studies, SNe II form a continuous population of objects from the colour point of view as well. We investigate correlations between the observed colours and a range of photometric and spectroscopic parameters including the absolute magnitude, the V-band light-curve slopes, and metal-line strengths. We find that less luminous SNe II appear redder, a trend that we argue is not driven by uncorrected host-galaxy reddening. While there is significant dispersion, we find evidence that redder SNe II (mainly at early epochs) display stronger metal-line equivalent widths. Host-galaxy reddening does not appear to be a dominant parameter, neither driving observed trends nor dominating the dispersion in observed colours. Intrinsic SN II colours are most probably dominated by photospheric temperature differences, with progenitor metallicity possibly playing a minor role. Such temperature differences could be related to differences in progenitor radius, together with the presence or absence of circumstellar material close to the progenitor stars.