We perform numerical simulations of clouds in the Galactic Centre (GC) engulfing the nuclear super-massive black hole and show that this mechanism leads to the formation of gaseous accretion discs with properties that are similar to the expected gaseous progenitor discs that fragmented into the observed stellar disc in the GC. As soon as the cloud hits the black hole, gas with opposite angular momentum relative to the black hole collides downstream. This process leads to redistribution of angular momentum and dissipation of kinetic energy, resulting in a compact gaseous accretion disc. A parameter study using thirteen high resolution simulations of homogeneous clouds falling onto the black hole and engulfing it in parts demonstrates that this mechanism is able to produce gaseous accretion discs that could potentially be the progenitor of the observed stellar disc in the GC. A comparison of simulations with different equations of state (adiabatic, isothermal and full cooling) demonstrates the importance of including a detailed thermodynamical description. However the simple isothermal approach already yields good results on the radial mass transfer and accretion rates, as well as disc eccentricities and sizes. We find that the cloud impact parameter strongly influences the accretion rate whereas the impact velocity has a small affect on the accretion rate.