No one has yet managed to answer why the reading is different open ring and closed ring.
I have given an example based on info from your earlier posts of how a live conductor with insulation damaged making contact with a nail or metal capping, metal studwork or other non-electrical metal parts fixed to the fabric of the building would cause different readings to E depending upon which parts are open/closed, and/or connected at CU or not...
And as UNG mentioned nails touching but not piercing a cable conductor... Picture hook, dado rail fixing, Christmas decoration hanging point... etc.. etc.. .can cause all sorts of weird readings..
As you haven't provided a comprehensive list of test results around the whole circuit..
Including continuity measurements at every outlet point and IR's for each section of cable..
anything else is just a bit of guesswork.
Personally with these sort of problems I find you can get yourself tied up in knots forgetting exactly what you have or haven't tested...
Normally I find it best to get back to basics and identify exactly how the circuit is wired...
Then start from the CU down one leg of the ring measuring and noting everything on an A4 pad..
Room / Socket / L to E and N to E continuity's check they match / IR between everything L-N, L-E, N-E..
etc.. etc.. around every outlet on the circuit that you can find..
Then as you work your way around the ring something normally crops up as clearly incorrect and points you to the cause of your dodgy reading(s)...
Some I have found have clearly been there for years... but as no PIR's have been done..
And as everything was still "Working" the customer was oblivious..
In your specific case where you have left it with the customer "seeing how it all goes" re further RCD tripping..
I would have ready a copy of Best Practice 4 recommendations...
And if you are called back say that you need a full days labour to do more comprehensive testing around the whole circuit..
During which time you may be able to resolve the problem..
Or it may need further labour and materials to resolve based upon what your further testing reveals..?
During these sort of tests I get very meticulous with my measurements, especially continuity along ALL conductors making sure they are ALL proportional to the expected cable lengths.. [L-N, L-E & N-E],
As dodgy readings are often an indication of: Bad joints, Nails in cables, Squashed conductors.. Damp, Rodents influences etc..
Without further circuit detail info and more test readings, I think we are all second guessing this one?
Have you verified that there are NO crossed circuits / borrowed neutrals / shared earths??
e.g. I've seen a conservatory take its lights 'Live' from the from the lighting circuit..
but neutral from the sockets.. Cant remember where the Earth came from..?
But it caused a few testing head-scratching moments until it was tracked down!!!!