We report on a sequence of field-induced transitions in the zigzag ladder compound BaDy2O4 studied with powder neutron diffraction and magnetisation measurements. In agreement with the previously published results, the low temperature zero-field structure is characterised by two half-integer propagation vectors, k1=[1/2 0 1/2] and k2= 1/2 1/2 1/2]. However, on application of an external magnetic field, the Bragg peaks corresponding to the zero-field structure lose their intensity rather rapidly and disappear completely in a field of 2.5 kOe. In the intermediate fields, 2.5 to 22.5 kOe, new peaks are observed characterised by the propagation vector k0=[0 0 1/3] corresponding to an up-up-down (uud) structure as well k=0 ferromagnetic peaks. This regime of fields corresponds to a pronounced plateau in the magnetisation curve. Remarkably, the uud structure survives heating to at least 1.4 K, three times higher temperature than the TN of 0.48 K for the zero-field structure. Above 22.5 kOe, the k0 peaks disappear while the k = 0 peaks gain significant intensity indicating an increase in the polarisation of the system. The analysis of the intensities of the field-induced reflections allows for a clear identification of the magnetic structures in both the intermediate and high field regimes.