We examine a sample of 48 Swift/UVOT long gamma-ray burst light curves and find a correlation between the logarithmic luminosity at 200 s and average decay rate determined from 200 s onwards, with a Spearman rank coefficient of −0.58 at a significance of 99.998 per cent (4.2σ). We discuss the causes of the log L200 s–α>200 s correlation, finding it to be an intrinsic property of long gamma-ray bursts, and not resulting from the selection criteria. We find two ways to produce the correlation. One possibility is that there is some property of the central engine, outflow or external medium that affects the rate of energy release so that the bright afterglows release their energy more quickly and decay faster than the fainter afterglows. Alternatively, the correlation may be produced by variation of the observer’s viewing angle, with observers at large viewing angles observing fainter and slower decaying light curves.