Context. Determining the average fraction of Lyman continuum (LyC) photons escaping high redshift galaxies is essential for understanding how reionization proceeded in the z> 6 Universe. Aims. We want to measure the LyC signal from a sample of sources in the Chandra Deep Field South (CDFS) and COSMOS fields for which ultra-deep VIMOS spectroscopy as well as multi-wavelength Hubble Space Telescope (HST) imaging are available. Methods. We select a sample of 46 galaxies at z ~ 4 from the VIMOS Ultra Deep Survey (VUDS) database, such that the VUDS spectra contain the LyC part, that is, the rest-frame range 880−910 Å. Taking advantage of the HST imaging, we apply a careful cleaning procedure and reject all the sources showing nearby clumps with different colours, that could potentially be lower-redshift interlopers. After this procedure, the sample is reduced to 33 galaxies. We measure the ratio between ionizing flux (LyC at 895 Å) and non-ionizing emission (at ~ 1500 Å) for all individual sources. We also produce a normalized stacked spectrum of all sources. Results. Assuming an intrinsic average Lν(1470) /Lν(895) of 3, we estimate the individual and average relative escape fraction. We do not detect ionizing radiation from any individual source, although we identify a possible LyC emitter with very high Lyα equivalent width (EW). From the stacked spectrum and assuming a mean transmissivity for the sample, we measure a relative escape fraction f escrel = 0.09 ± 0.04. We also look for correlations between the limits in the LyC flux and source properties and find a tentative correlation between LyC flux and the EW of the Lyα emission line. Conclusions. Our results imply that the LyC flux emitted by V = 25−26 star-forming galaxies at z ~ 4 is at most very modest, in agreement with previous upper limits from studies based on broad and narrow band imaging.