Lopsidedness of the gaseous disc of spiral galaxies is a common phenomenon in disc morphology, profile and kinematics. Simultaneously, the asymmetry of a galaxy's stellar disc, in combination with other morphological parameters, has seen extensive use as an indication of recent merger or interaction in galaxy samples. Quantified morphology of stellar spiral discs is one avenue to determine the merger rate over much of the age of the Universe. In this paper, we measure the quantitative morphology parameters for the H I column density maps from the Westerbork observations of neutral Hydrogen in Irregular and SPiral galaxies (WHISP). These are Concentration, Asymmetry, Smoothness, Gini, M-20 and one addition of our own, the Gini parameter of the second-order moment (GM). Our aim is to determine if lopsided or interacting discs can be identified with these parameters. Our sample of 141 H I maps have all previous classifications on their lopsidedness and interaction.We find that the Asymmetry, M-20 and our new G(M) parameter correlate only weakly with the previous morphological lopsidedness quantification. These three parameters may be used to compute a probability that an H I disc is morphologically lopsided but not unequivocally to determine it. However, we do find that the question whether or not an H I disc is interacting can be settled well using morphological parameters. Parameter cuts from the literature do not translate from ultraviolet to H I directly but new selection criteria using combinations of Asymmetry and M-20 or Concentration and M-20 work very well.We suggest that future all-sky H I surveys may use these parameters of the column density maps to determine the merger fraction and hence rate in the local Universe with a high degree of accuracy.