During an extensive multiwavelength campaign that we performed in 2013-14 the prototypical Seyfert 1 galaxy NGC 5548 has been found in an unusual condition of heavy and persistent obscuration. The newly discovered obscurer absorbs most of the soft X-ray continuum along our line of sight and lowers the ionizing luminosity received by the classical warm absorber. Here we present the analysis of the high resolution X-ray spectra collected with XMM-Newton and Chandra throughout the campaign, which are suitable to investigate the variability of both the obscurer and the classical warm absorber. The time separation between these X-ray observations range from 2 days to 8 months. On these timescales the obscurer is variable both in column density and in covering fraction. This is consistent with the picture of a patchy wind. The most significant variation occurred in September 2013 when the source brightened for two weeks. A higher and steeper intrinsic continuum and a lower obscurer covering fraction are both required to explain the spectral shape during the flare. We suggest that a geometrical change of the soft X-ray source behind the obscurer cause the observed drop in the covering fraction. Due to the higher soft X-ray continuum level the September 2013 Chandra spectrum is the only X ray spectrum of the campaign where individual features of the warm absorber could be detected. The spectrum shows absorption from Fe-UTA, ion{O}{iv}, and ion{O}{v}, consistent to belong to the lower-ionization counterpart of the historical NGC 5548 warm absorber. Hence, we confirm that the warm absorber has responded to the drop in the ionizing luminosity caused by the obscurer.
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