In this article, a system of amyloid fibrils, based on the protein beta-lactoglobulin, is studied by transient electric birefringence. Single pulses of an electric field were applied to the solution, and the initial rise and subsequent decay of birefringence analysed. The decay takes place on a range of relaxation times, and therefore contains information about the length distribution of fibrils in the system. The information can be extracted using theories of the electric polarisability of polyelectrolyte rods, since the fibrils are an example of these. Despite the long-standing complications of such theories, useful quantitative information about the system can still be obtained. Using the Fixman model of polyelectrolyte polarisability, we obtain a measurement of the short end of the length distribution which shows the fibril concentration as a function of length rising linearly from 0.02-2 microm. The short end of the length distribution was unobtainable in our previous study using rheo-optics (S.S. Rogers et al., Macromolecules 38, 2948 (2005)), but reasonable agreement between the two techniques shows they are complementary.