Hydrogen Lyα haloes (LAHs) are commonly used as a tracer of the circumgalactic medium (CGM) at high redshifts. In this work, we aim to explore the existence of Lyα haloes around individual UV-selected galaxies, rather than around Lyα emitters (LAEs), at high redshifts. Our sample was continuum-selected with F775W ≤ 27.5, and spectroscopic redshifts were assigned or constrained for all the sources thanks to the deepest (100- to 140-h) existing Very Large Telescope (VLT)/Multi-Unit Spectroscopic Explorer (MUSE) data with adaptive optics. The final sample includes 21 galaxies that are purely F775W-magnitude selected within the redshift range z ≈ 2.9 − 4.4 and within a UV magnitude range −20 ≤ M1500 ≤ −18, thus avoiding any bias toward LAEs. We tested whether galaxy’s Lyα emission is significantly more extended than the MUSE PSF-convolved continuum component. We find 17 LAHs and four non-LAHs. We report the first individual detections of extended Lyα emission around non-LAEs. The Lyα halo fraction is thus as high as 81.0−11.2+10.3%, which is close to that for LAEs at z = 3 − 6 in the literature. This implies that UV-selected galaxies generally have a large amount of hydrogen in their CGM. We derived the mean surface brightness (SB) profile for our LAHs with cosmic dimming corrections and find that Lyα emission extends to 5.4 arcsec (≃40 physical kpc at the midpoint redshift z = 3.6) above the typical 1σ SB limit. The incidence rate of surrounding gas detected in Lyα per one-dimensional line of sight per unit redshift, dn/dz, is estimated to be 0.76−0.09+0.09 for galaxies with M1500 ≤ −18 mag at z ≃ 3.7. Assuming that Lyα emission and absorption arise in the same gas, this suggests, based on abundance matching, that LAHs trace the same gas as damped Lyα systems (DLAs) and sub-DLAs.Key words: galaxies: high-redshift / galaxies: formation / galaxies: evolution / galaxies: halos / cosmology: observations⋆ Based on observations made with ESO telescope at the La Silla Paranal Observatory under the large program 1101.A-0127.