The next generation of neutrino telescopes will feature unprecedented sensitivities in the detection of neutrinos. Here we study the capabilities of a large-scale neutrino telescope, like the fully-operating KM3NeT experiment in the near future, for detecting dark matter annihilation signals from the Galactic Centre. We consider both ORCA and ARCA detectors, covering dark matter masses from a few GeV to 100 TeV. We obtain the sensitivities with a maximum-likelihood analysis method and present them as upper limits in the thermally averaged annihilation cross-section into Standard Model fermions. Our projections show that the sensitivity of such a neutrino telescope can reach the thermal relic line for m χ≳ 1 TeV and for m χ≃ few GeV, for the NFW dark matter density profile. This demonstrates that ORCA-and ARCA-like detectors will be able to perform competitive dark matter searches in a wide range of masses. The implications of these striking projections are investigated in a few selected dark matter particle models, where we show that neutrino telescopes are able to probe new parameter space.