We present a direct measurement of the low-energy 8 Li(p, α) 5 He cross section, using a radioactive 8 Li beam impinging on a thick target. With four beam energies, we cover the energy range between E c.m. = 0.2 and 2.1 MeV. An R-matrix analysis of the data is performed and suggests the existence of two broad overlapping resonances (5/2+ at E c.m. = 1.69 MeV and 7/2 + at E c.m. = 1.76 MeV). At low energies our data are sensitive to the properties of a subthreshold state (E x = 16.67 MeV) and of two resonances above threshold. These resonances were observed in previous experiments. The R-matrix fit confirms spin assignments, and provides partial widths. We propose a new 8 Li(p, α) 5 He reaction rate and briefly discuss its influence in nuclear astrophysics.