We examine the properties of barred disc galaxies in a ΛCDM cosmological hydrodynamical simulation from the EAGLE project. Our study follows the formation of 269 discs identified at z = 0 in the stellar mass range 10.6 < log M*/M⊙ < 11. These discs show a wide range of bar strengths, from unbarred discs (≈60 per cent) to weak bars (≈20 per cent) and to strongly barred systems (≈20 per cent). Bars in these systems develop after redshift ≈1.3, on time-scales that depend sensitively on the strength of the pattern. Strong bars develop relatively quickly (in a few Gyr, or roughly ∼10 disc rotation periods) in systems that are disc dominated, gas poor, and have declining rotation curves. Weak bars develop more slowly in systems where the disc is less gravitationally important, and are still growing at z = 0. Unbarred galaxies are comparatively gas-rich discs whose rotation speeds do not exceed the maximum circular velocity of the haloes they inhabit. Bar lengths compare favourably with observations, ranging from 0.2 to 0.8 times the radius containing 90 per cent of the stars. Bars slow down remarkably quickly as they grow, causing the inner regions of the surrounding dark halo to expand. At z = 0 strong bars in simulated galaxies have corotation radii roughly 10 times the bar length. Such slow bars are inconsistent with the few cases where pattern speeds have been measured or inferred observationally, a discrepancy that, if confirmed, might prove a challenge for disc galaxy formation in ΛCDM.