Saturn's moon Enceladus emits plumes of water vapour and ice particles from fractures near its south pole, suggesting the possibility of a subsurface ocean. These plume particles are the dominant source of Saturn's E ring. A previous in situ analysis of these particles concluded that the minor organic or siliceous components, identified in many ice grains, could be evidence for interaction between Enceladus' rocky core and liquid water. It was not clear, however, whether the liquid is still present today or whether it has frozen. Here we report the identification of a population of E-ring grains that are rich in sodium salts ( approximately 0.5-2% by mass), which can arise only if the plumes originate from liquid water. The abundance of various salt components in these particles, as well as the inferred basic pH, exhibit a compelling similarity to the predicted composition of a subsurface Enceladus ocean in contact with its rock core. The plume vapour is expected to be free of atomic sodium. Thus, the absence of sodium from optical spectra is in good agreement with our results. In the E ring the upper limit for spectroscopy is insufficiently sensitive to detect the concentrations we found.