We present experiments using relativistic-intensity 1.5-cycle laser fields at 1 kHz repetition rate to drive surface high-harmonic generation (SHHG) from surface plasmas with controlled density gradient. As a function of the driving pulse carrier-envelope phase (CEP), we observe a transition from a modulated to a continuous SHHG spectrum, indicating the transition from double to isolated attosecond pulse emission. Single shot-acquisitions of XUV spectral continua support the emission of isolated attosecond pulses with an isolation degree of between 10 and 50 for the majority of the driving pulse CEPs. 2D Particle-in-cell simulations corroborate this interpretation and predict percent-level efficiencies for the generation of an isolated attosecond pulse even without spectral filtering.