Recent and on-going large ground-based multi-object spectroscopic surveys allow to significantly increase the sample of spectroscopic binaries to get insight into their statistical properties. We investigate the repeated spectral observations of the Gaia-ESO Survey (GES) internal data release 5 to identify and characterize spectroscopic binaries with one visible component (SB1) in fields covering the discs, the bulge, the CoRot fields, and stellar clusters and associations. A statistical chi2-test is performed on spectra of the iDR5 sub-sample of approximately 43500 stars characterized by at least 2 observations and a S/N>3. Our sample of RV variables is cleaned from contamination by pulsation/convection-induced variables using Gaia DR2 parallaxes and photometry. Monte-Carlo simulations using the SB9 catalogue of spectroscopic orbits allow to estimate our detection efficiency and to correct the SB1 rate to evaluate the GES SB1 binary fraction and its dependence with effective temperature and metallicity. We find 641 (resp., 803) FGK SB1 candidates at the 5 sigma (resp., 3 sigma) level. The orbital-period distribution is estimated from the RV standard-deviation distribution and reveals that the detected SB1 probe binaries with log(P[d]) < 4. We estimate the global GES SB1 fraction to be in the range 7-14% with a typical uncertainty of 4%. The GES SB1 frequency decreases with metallicity at a rate of -9+/-3%/dex in the metallicity range -2.7<FeH<+0.6. This anticorrelation is obtained with a confidence level higher than 93% on a homogeneous sample covering spectral types FGK and a large range of metallicities. When the present-day mass function is accounted for, this rate turns to 4+/-2%/dex with a confidence level higher than 88%. In addition we provide the variation of the SB1 fraction with metallicity separately for F, G, and K spectral types, as well as for dwarf and giant primaries.