If I turn off the downstairs ring at the breaker and check Live-earth and
Neutral-earth with a crude tester, I get no indication of voltage flow.

No such thing as voltage flow. Step away from the crude tester. Someone
might get hurt.

If I accidentally dab live or neutral to earth, then it knocks out the
RCD.
So where is the current flow being generated which will trip the RCD when
the live is isolated at the breaker?

It goes from the live of the "on" circuit, through an appliance to neutral
on the "on" circuit. This is connected directly to the neutral of the "off"
circuit, through an appliance on the "off" circuit into the live of the
"off" circuit and into the earth of the "off" circuit and into the ground.
There are two appliances worth of resistance, but it can be enough to trip
an RCD.

It is more likely on a neutralearth leak on the "off" circuit, as there is
no need to get through an appliance to get to the shorted live.

Christian.