An anomalous flux of neutrinos produced in hypothetical annihilations or decays of dark matter inside a source would produce a signal observable with neutrino telescopes. As suggested by observations, a conspicuous amount of dark matter is believed to accumulate in the centre of our Galaxy, which is in neat visibility for the Mediterranean underwater telescopes ANTARES and KM3NeT. Searches have been conducted with a maximum likelihood method to identify the presence of a dark matter signature in the neutrino flux measured by ANTARES. Results of all-flavour searches for WIMPs with masses from 50 GeV/c2 up to 100 TeV/c2 over the whole operation period from 2007 to 2020 are presented here. The presentation of Galactic Centre searches is completed with ongoing analyses and future potential of the KM3NeT telescope, in phased construction in the Mediterranean Sea.