The diffusion coefficient, D, of a typical UV-absorbing stabiliser has been measured in a series of poly(ester-block-ether) copolymers (PEBEs) with different fractions of the polyether blocks, by using ultra-violet microscopy to monitor the concentration profile of the additive diffused into the edge of a thin film of polymer over a range of temperatures. For all samples, D shows an Arrhenius dependence on temperature over the range studied. At a given temperature, D increases rapidly with the polyether content, showing a percolation threshold and a marked drop in activation energy at 30 wt% polyether. This is consistent with the view that D is higher in the polyether than in the polyester and that there is a change in morphology at the percolation threshold, from isolated particles of the polyether to a co-continuous morphology with percolation paths of polyether. Comparison with data for the same permeant in polypropylene shows differences, which can be accounted for at least qualitatively by a free-volume argument.