The present study analyses the influence of topography, β-effect, and the gradient of the meridional variability of the background current on the barotropic topographic Rossby waves. We exclude the stratification effect from the problem and consider a vertically integrated zonal flow because the previous results show that short waves are seldom, and the stratification effect on long Rossby waves is insignificant. We consider the transverse (meridional) variability of the background topography current in the WKB approximation. Thus, we obtain a dispersion relation for plane barotropic topographic Rossby waves, which simultaneously accounts for the effects of the Earth's rotation, velocity shear, and topography. The GLORYS12v1 product for the Antarctic Circumpolar Current zone is used to calculate the current velocity shift. The topography structure is modeled as an elongated ridge and approximated by an exponential and a Gaussian function with different parameters. The results show that the contribution of the shear flow can overlap the contribution of topography locally. The topographic factor in the dispersion relation is dominant. Specifically, in the southern hemisphere, on the northern side of the ridge, the impact of topography on the Rossby waves intensifies due to the β-effect, while, on the southern side, it reduces due the β-effect.