ABSTRACT We present the results of a new study investigating the relationship between observed Ly α equivalent width (Wλ(Ly α)) and the metallicity of the ionizing stellar population ( Z⋆) for a sample of 768 star-forming galaxies at 3 ≤ z ≤ 5 drawn from the VANDELS survey. Dividing our sample into quartiles of rest-frame Wλ(Ly α) across the range $-58 \,\rm {\mathring{\rm A}} \lesssim$Wλ(Ly α) $\lesssim 110 \,\rm {\mathring{\rm A}}$, we determine  Z⋆ from full spectral fitting of composite far-ultraviolet spectra and find a clear anticorrelation between Wλ(Ly α) and  Z⋆. Our results indicate that  Z⋆ decreases by a factor ≳ 3 between the lowest Wλ(Ly α) quartile (〈Wλ(Ly α)$\rangle =-18\,\rm {\mathring{\rm A}}$) and the highest Wλ(Ly α) quartile (〈Wλ(Ly α)$\rangle =24\,\rm {\mathring{\rm A}}$). Similarly, galaxies typically defined as Lyman alpha emitters (LAEs; Wλ(Ly α) $\gt 20\,\rm {\mathring{\rm A}}$) are, on average, metal poor with respect to the non-LAE galaxy population (Wλ(Ly α) $\le 20\,\rm {\mathring{\rm A}}$) with  Z⋆non-LAE ≳ 2 ×  Z⋆LAE. Finally, based on the best-fitting stellar models, we estimate that the increasing strength of the stellar ionizing spectrum towards lower  Z⋆ is responsible for ${\simeq}15{-}25{{\ \rm per\ cent}}$ of the observed variation in Wλ(Ly α) across our sample, with the remaining contribution (${\simeq}75{-}85{{\ \rm per\ cent}}$) being due to a decrease in the H i/dust covering fractions in low- Z⋆ galaxies.