We present results on the radiation drag exerted by an isotropic and homogenous background of Lya photons on neutral gas clouds orbiting within HII regions around Population III stars of different masses. The Doppler shift causes a frequency difference between photons moving in the direction of the cloud and opposite to it resulting in a net momentum loss of the cloud in the direction of motion. We find that half of the angular momentum of gas with v_theta <~ 20 km/s near (r <~ 3 kpc) a Population III star of 120 Msun at z=20 is lost within ~ 10^6 yr. The radiation drag is a strong function of cloud velocity that peaks at v ~ 20 km/s reflecting the frequency dependence of the photon cross section. Clouds moving with velocities larger than ~ 100 km/s loose their angular momentum on time scales of ~ 10^8 yr. At lower redshifts radiation drag becomes inefficient as the Lya photon density in HII regions decreases by a factor (1+z)^3 and angular momentum is lost on time scales > 10^8 yr even for low velocity clouds. Our results suggest that a sweet spot exists for the loss of angular momentum by radiation drag for gas clouds at z > 10 and with v ~ 20 km/s. Comparison to dynamical friction forces acting on typical gas clouds suggest that radiation drag is the dominant effect impacting the orbit. We propose that this effect can suppress the formation of extended gas discs in the first galaxies and help gas accretion near galactic centres and central black holes.