Using high-resolution SPH simulations in a fully cosmological Λ cold dark matter context, we study the formation of a bright disc-dominated galaxy that originates from a 'wet' major merger at z= 0.8 . The progenitors of the disc galaxy are themselves disc galaxies that formed from early major mergers between galaxies with blue colours. A substantial thin stellar disc grows rapidly following the last major merger and the present-day properties of the final remnant are typical of early-type spiral galaxies, with an i-band bulge-to-disc ratio ∼0.65, a disc scalelength of 7.2 kpc, g−r= 0.5 mag , an H i linewidth (W20/2) of 238 km s−1 and total magnitude i=−22.4 . The key ingredients for the formation of a dominant stellar disc component after a major merger are (i) substantial and rapid accretion of gas through cold flows followed at late times by cooling of gas from the hot phase, (ii) supernova feedback that is able to partially suppress star formation during mergers and (iii) relative fading of the spheroidal component. The gas fraction of the progenitors' discs does not exceed 25 per cent at z < 3 , emphasizing that the continuous supply of gas from the local environment plays a major role in the regrowth of discs and in keeping the galaxies blue. The results of this simulation alleviate the problem posed for the existence of disc galaxies by the high likelihood of interactions and mergers for galaxy-sized haloes at relatively low z.