This paper is concerned with the boundary layer on the leading edge of an aerofoil with the aerofoil surface sliding parallel to itself in the upstream direction. The flow analysis is conducted in the framework of the classical Prandtl formulation with the pressure distribution given by the solution for the outer inviscid flow. Since a reverse flow region is always present near the wall, a numerical method, where the derivatives were approximated by the windward finite differences, was used to solve the boundary-layer equations. We were interested in the flow behaviour on the upper surface of the aerofoil, but to calculate the boundary-layer equations, we had to extend the computational domain from the upper surface of the aerofoil to the lower surface. The calculations were performed for a range of angles of attack, and it is found that there exists a critical value of the angle of attack for which the Moore–Rott–Sears singularity forms in the flow. This is accompanied by an abrupt thickening of the boundary layer at the singular point and the formation of a recirculation region with closed streamlines behind this point. We further found that the flow immediately behind the singular point and in the recirculation region could be treated as inviscid, which allowed us to use the Prandtl–Batchelor theorem for theoretical modelling of the flow. A similar formulation was used earlier by Bezrodnykh et al. (Comput. Maths Math. Phys. vol. 63, 2023, pp. 2359–2371). These authors considered the boundary-layer flow on a flat plate with the pressure gradient created by a dipole situated some distance from the plate. They also found that there exists a critical value of the dipole strength for which a singularity forms in the boundary layer. However, their interpretation of the flow behaviour differs significantly from what we observe in our study.