Context. Our consortium performed an extensive multi-wavelength campaign of the nearby Seyfert 1 galaxy NGC 5548 in 2013-14. The source appeared unusually heavily absorbed in the soft X-rays, and signatures of outflowing absorption were also present in the UV. He-like triplets of neon, oxygen and nitrogen, and radiative recombination continuum (RRC) features were found to dominate the soft X-ray spectrum due to the low continuum flux. Aims. Here we focus on characterising these narrow emission features using data obtained from the XMM-Newton RGS (770 ks stacked spectrum). Methods. We use SPEX for our initial analysis of these features. Self-consistent photoionisation models from Cloudy are then compared with the data to characterise the physical conditions of the emitting region. Results. Outflow velocity discrepancies within the O VII triplet lines can be explained if the X-ray narrow-line region (NLR) in NGC 5548 is absorbed by at least one of the six warm absorber components found by previous analyses. The RRCs allow us to directly calculate a temperature of the emitting gas of a few eV ($∼10^{4}$ K), favouring photoionised conditions. We fit the data with a Cloudy model of log $ξ = 1.45 ± 0.05$ erg cm s$^{-1}$, log $N_H = 22.9 ± 0.4$ cm$^{-2}$ and log v$_{turb} = 2.25 ± 0.5$ km s$^{-1}$ for the emitting gas; this is the first time the X-ray NLR gas in this source has been modelled so comprehensively. This allows us to estimate the distance from the central source to the illuminated face of the emitting clouds as $13.9 ± 0.6$ pc, consistent with previous work. ; Comment: Accepted by A&A, 15 pages, 6 figures