The differential cross-section of prompt inclusive production of long-lived charged particles in proton-proton collisions is measured using a data sample recorded by the LHCb experiment at a centre-of-mass energy of $s=13\mathrm{TeV}$. The data sample, collected with an unbiased trigger, corresponds to an integrated luminosity of $5.4\mathrm{nb}-1$. The differential cross-section is measured as a function of transverse momentum and pseudorapidity in the ranges $pT\in [0.08,10)\mathrm{GeV}c-1$ and $\eta \in [2.0,4.8)$ and is determined separately for positively and negatively charged particles. The results are compared with predictions from various hadronic-interaction models.