  We present a survey of $z\sim3$ Ly$\alpha$ emitters (LAEs) within the fields
of the VLT LBG Redshift Survey. The data encompasses 5 independent survey
fields co-spatial with spectroscopic LBG data and covering a larger total area
than previously analysed for LAE number counts and clustering. This affords an
improved analysis over previous work by minimising the effects of cosmic
variance and allowing the cross-clustering analysis of LAEs and LBGs. Our
photometric sample consists of $\approx600$ LAE candidates, over an area of
1.07~deg$^2$, with equivalent widths of $\gtrsim65$~\AA\ and a flux limit of
$\approx2\times10^{-17}$~erg~cm$^{-2}$~s$^{-1}$. From spectroscopic follow-up,
we measured a success rate of $78\pm18\%$. We find the $R$-band continuum
luminosity function to be $\sim10\times$ lower than the luminosity function of
LBGs at this redshift, consistent with previous studies. Exploiting the large
area of the survey, we estimate the LAE auto-correlation function and find a
clustering length of $r_0=2.86\pm0.33~h^{-1}$~Mpc, low compared to the $z\sim3$
LBG population, but somewhat higher than previous LAE measurements. This
corresponds to a median halo mass of $M_{\rm
DM}=10^{11.0\pm0.3}~h^{-1}~$M$_{\odot}$. We present an analysis of clustering
length versus continuum magnitude and find that the measurements for LAEs and
LBGs are consistent at faint magnitudes. Our combined dataset of LAEs and LBGs
allows us to measure, for the first time, the LBG-LAE cross-correlation,
finding a clustering length of $r_0=3.29\pm0.57~h^{-1}$~Mpc and a LAE halo mass
of $10^{11.1\pm0.4}~h^{-1}$~M$_{\odot}$. Overall, we conclude that LAEs inhabit
primarily low mass halos, but form a relatively small proportion of the galaxy
population found in such halos.
