Although ultraviolet (UV) light is important in many areas of science and technology, there are very few if any lasers capable of delivering wavelength-tunable ultrashort UV pulses at MHz repetition rates. Here we report the generation of deep-UV laser pulses at MHz repetition rates and mu J-energies by means of dispersive wave (DW) emission from self-compressed solitons in gas-filled single-ring hollow-core photonic crystal fiber (SR-PCF). Pulses from an ytterbium fiber laser (~300 fs) are first compressed to ~25 fs in a SR-PCF-based nonlinear compression stage, and subsequently used to pump a second SR-PCF stage for broadband DW generation in the deep UV. The UV wavelength is tunable by selecting the gas species and the pressure. At 100 kHz repetition rate, a pulse energy of 1.05 mu J was obtained at 205 nm (average power 0.1 W), and at 1.92 MHz, a pulse energy of 0.54 mu J was obtained at 275 nm (average power 1.03 W).