Continuity issue

On a ring main I have no continuity end to end on the live conductor but is ok on neutral and earth. When I connect EITHER live conductor to the supply ALL the sockets go live with the correct polarity. My brain is telling me that this is not possible. What the hell am I missing?

What are you using to determine "they all go live"?

My guess would be a high resistance connection somewhere and if you went round with a load that drew some current, e.g. a small heater, you would soon find half your ring the voltage drops like a stone when you plug the load in and would help you track down where the poor connection is.

I would recommend you both R1 + R2 on both legs from the CU and make a note of each reading at each socket then see what results you get. This may give you some pointers

 I’m thinking poor connection at a socket 

What are you measuring continuity with?  i.e. could the still be some continuity but Off range?

What are your actual readings for  N->N   E->E?

Have you done an IR tests between the two 'L' conductors?

I assume this is an old existing circuit? not a new install?

Think you need to ignore your "live" testing method, and get back to basics with dead testing the whole circuit.

I would probably disconnect all conductors from both ends of the ring at the CU..

So its all fully isolated and make sure all loads are disconnected..

Then for my own curiosity to establish the order the circuit is wired in, I would temp measure it as if was a radial..

i.e.  Join L,N,E of the one cable all together into a WAGO, leave the other cable all open..

and go round measuring at every socket, between L->E, N->E, L->N.

Checking they all appear proportional to each other with respect to the estimated cable lengths/conductor sizes between each outlet...

Key point to remember is... You could have multiple loose connections around the ring..

And 240v electricity can bridge some quite poor joints causing all sorts of potential faults if not fixed.

So prove the whole circuit 100% dead first..

then start re-energising doing live tests.