We present very high spatial resolution deep radio continuum observations at 5 GHz (6 cm) made with e-MERLIN of the young stars DG Tau A and B. Assuming it is launched very close (~=1 au) from the star, our results suggest that the DG Tau A outflow initially starts as a poorly focused wind and undergoes significant collimation further along the jet (~=50 au). We derive jet parameters for DG Tau A and find an initial jet opening angle of 86 degrees within 2 au of the source, a mass-loss rate of 1.5x10^-8 solar masses/yr for the ionised component of the jet, and the total ejection/accretion ratio to range from 0.06-0.3. These results are in line with predictions from MHD jet-launching theories.