In 2013, we conducted a large multi-wavelength campaign on the archetypical Seyfert 1 galaxy NGC 5548. Unexpectedly, this usually unobscured source appeared strongly absorbed in the soft X-rays during the entire campaign, and signatures of new and strong outflows were present in the almost simultaneous UV HST/COS data. Here we carry out a comprehensive spectral analysis of all available XMM-Newton observations of NGC 5548 (precisely 14 observations from our campaign plus three from the archive, for a total of ∼763 ks) in combination with three simultaneous NuSTAR observations. We obtain a best-fit underlying continuum model composed by i) a weakly varying flat (Γ ∼ 1.5-1.7) power-law component; ii) a constant, cold reflection (FeK + continuum) component; iii) a soft excess, possibly owing to thermal Comptonization; and iv) a constant, ionized scattered emission-line dominated component. Our main findings are that, during the 2013 campaign, the first three of these components appear to be partially covered by a heavy and variable obscurer that is located along the line of sight (LOS), which is consistent with a multilayer of cold and mildly ionized gas. We characterize in detail the short timescale (mostly ∼ks-to-days) spectral variability of this new obscurer, and find it is mostly due to a combination of column density and covering factor variations, on top of intrinsic power-law (flux and slope) variations. In addition, our best-fit spectrum is left with several (but marginal) absorption features at rest-frame energies ∼6.7−6.9 keV and ∼8 keV, as well as a weak broad emission line feature redwards of the 6.4 keV emission line. These could indicate a more complex underlying model, e.g. a P-Cygni-type emission profile if we allow for a large velocity and wide-angle outflow. These findings are consistent with a picture where the obscurer represents the manifestation along the LOS of a multilayer of gas, which is also in multiphase, and which is likely outflowing at high speed, and simultaneously producing heavy obscuration and scattering in the X-rays, as well as broad absorption features in the UV.