We analysed data from five XMM-Newton observations of GX 13+1 to investigate the variability of the photo-ionised absorber present in this source. We fitted EPIC and RGS spectra obtained from the least-variable intervals with a model consisting of disc-blackbody and blackbody components together with a Gaussian emission feature at ~6.55-6.7 keV modified by absorption due to cold and photo-ionised material. We found a significant correlation between the hard, ~6-10 keV, flux, the ionisation and column density of the absorber and the equivalent width of the broad iron line. We interpret the correlation in a scenario in which a disc wind is thermally driven at large, ~10^{10} cm, radii and the broad line results from reprocessed emission in the wind and/or hot atmosphere. The breadth of the emission line is naturally explained by a combination of scattering, recombination and fluorescence processes. We attribute the variations in the absorption and emission along the orbital period to the view of different parts of the wind, possibly located at slightly different inclination angles. We constrain the inclination of GX 13+1 to be between 60 and 80 degrees from the presence of strong absorption in the line of sight, that obscures up to 80% of the total emission in one observation, and the absence of eclipses. We conclude that the presence of a disc wind and/or a hot atmosphere can explain the current observations of narrow absorption and broad iron emission features in neutron star low mass X-ray binaries as a class.
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