I'm not sure what you mean. Is it a short P to N?
You surely don't mean "resistance test between live conductors " as there is supposed to be continuity between them! And you can't mean N to E as they are (approximately) connected depending on earthing type.
After de-energising, I'd start by taking out the middle socket in the ring, to split it, then disconnecting at the CU, and seeing which half of the ring contains the short, then (personal choice) you can either work your way along that half, disconnecting and retesting at each socket, or (my preference) halve it again, and again, and again, until you find the part with the fault.
If you don't want to disconnect at the CU (e.g. crammed with cables), then take out the two sockets nearest the CU, as well as the middle one. that gives you two separate straight runs to investigate. The fewer things you disconnect the better, in my opinion, as you reduce the possibility of introducing new problems.
You'd also want to consider the age of the installation, and when the fault appeared - e.g. after nailing in new skirtings (probably a nail through a cable) or after fitting new socket (probably loose wire touching the backbox) or after plugging in new appliance (unplug it) or after fitting new CU (colourblind electrician)
