A new knee-like approximation of the lateral distribution function (LDF) of EAS Cherenkov light in the 30–3000 TeV energy range was proposed and tested with simulated showers in our earlier studies. This approximation fits the LDFs of individual showers accurately for all types of primary particles gamma-rays, protons, and nuclei) and is suitable for reconstructing the shower core, determining the energy, and separating gamma-induced showers from hadron-induced ones. In the present study, the knee-like fitting function is used to determine the parameters of real showers detected by TAIGA-HiSCORE. It is demonstrated that this approximation characterizes properly all types of individual LDFs of experimental events in the 300–1000 TeV range. The accuracy of fit is governed by fluctuations intrinsic to the process of measurement of the Cherenkov photon density. The probability density function of these fluctuations was reconstructed and introduced into simulations. Certain useful methodical applications of the knee-like approximation are con-sidered, and the possibility of shower sorting into nuclei groups is examined. The extensive statistical coverage and detailed LDF measurement data of HiSCORE have provided the first opportunity to examine in depth the LDF of Cherenkov radiation in the 300–1000 TeV range.