you probably have a broken ring. The test you are doing is not wrong, at any socket on a ring, there should be continuity between the two reds; and between the two blacks, and between the G&Ys (however continuity on earths is not such a good indictor of an unbroken ring, as it might be finding a path through supplementary bonding and water pipes).
If you do not find continuity, get a longish piece of wire and (with all power turned off!!) look for continuity from the terminals at the consumer unit, to each of the wires in each socket. You may find it easier to start at about the middle. Of course, you must reconnect each socket after you have tested it. Make a diagram of the house and sockets and mark what you find on each.
If you have a multimeter, measure and note the resistance you find, on each wire at each socket. You can expect the resistance to increase as you get further from the CU and nearer to the break in the ring.
p.s. It is possible that you do not have a proper ring; some of the sockets may have been wired on a radial running off the ring as a spur (this is wrong if there is more than one socket on the spur)