AlGaN/GaN heterostructure field effect transistors subject to UV illumination exhibit persistent photoconductivity both in the gate leakage and in the drain current. Time decay modelling of the gate photocurrent enables us to extract the surface potential transient. Simultaneous measurements of drain and gate currents indicate that (i) the gate leakage current negatively charges surface states, (ii) the large change in surface potential induced by UV illumination is responsible for the change in drain current in these devices. We present a detailed analytical model describing the gate and drain current decay transients, following UV illumination, in terms of surface potential modulation due to charging and discharging of surface traps. It is also found that for constant illumination and drain bias voltage conditions the change in the two-dimensional electron gas density is nearly constant independent of the gate bias. Using a previously measured mobility-carrier density relation we determine quantitatively the drain current transient.