In this Letter, we report the generation of a femtosecond supercontinuum extending from the ultraviolet to the near-infrared spectrum and detection of its carrier-envelope-phase (CEP) variation by f-to-2f interferometry. The spectrum is generated in a gas-filled hollow-core photonic crystal fiber, where soliton dynamics allows the CEP-stable self-compression of the optical parametric chirped-pulse amplifier pump pulses at 800 nm to a duration of 1.7 optical cycles, followed by dispersive wave emission. The source provides up to 1 μJ of pulse energy at the 800 kHz repetition rate, resulting in 0.8 W of average power, and it can be extremely useful, for example in strong-field physics, pump-probe measurements, and ultraviolet frequency comb metrology.