  We report evidence for the first generation of XUV spectra from relativistic
surface high-harmonic generation (SHHG) on plasma mirrors at a kilohertz
repetition rate, emitted simultaneously with energetic electrons. SHHG spectra
and electron angular distributions are measured as a function of the
experimentally controlled plasma density gradient scale length $L_\mathrm{g}$
for three increasingly short and intense driving pulses: 24~fs and $a_0=1.1$,
8~fs and $a_0=1.6$, and finally 4~fs and $a_0\approx2.1$, where $a_0$ is the
peak vector potential normalized by $m_\mathrm{e} c/e$ with the elementary
charge $e$, the electron rest mass $m_\mathrm{e}$, and the vacuum light
velocity $c$. For all driver pulses, we observe correlated relativistic SHHG
and electron emission in the range $L_\mathrm{g}\in[\lambda/25,\lambda/5]$,
with an optimum gradient scale length of $L_\mathrm{g}\approx\lambda/10$.
