The transport of non-thermal particles across a large-scale magnetic field in the presence of magnetised turbulence has been a long-standing issue in high-energy astrophysics. Of particular interest is the dependence of the parallel and perpendicular mean free paths $\lambda_{\parallel}$ and $\lambda_{\perp}$ on rigidity $\mathcal{R}$. We have revisited this important issue with a view to applications from the transport of Galactic cosmic rays. We have run test particle simulations of cosmic ray transport in synthetic, isotropic Kolmogorov turbulence at unprecedentedly low reduced rigidities $r_{\rm g}/L_c \simeq 10^{-4}$, corresponding to $\mathcal{R} \simeq 10 \, \text{TV}$ for a turbulent magnetic field of $B_{\rm rms} = 4 \, \mu\text{G}$ and correlation length $L_c = 30 \, \text{pc}$. Extracting the (asymptotic) parallel and perpendicular mean free paths $\lambda_{\parallel}$ and $\lambda_{\perp}$, we have found $\lambda_{\parallel} \propto (r_{\rm g}/L_c)^{1/3}$ as expected for a Kolmogorov turbulence spectrum. In contrast, $\lambda_{\perp}$ has a faster dependence on $r_{\rm g}/L_c$ for $10^{-2} \lesssim r_{\rm g}/L_c \lesssim 1$, but for $r_{\rm g}/L_c \ll 10^{-2}$, also $\lambda_{\perp} \propto (r_{\rm g}/L_c)^{1/3}$. Our results have important implications for the transport of Galactic cosmic rays.