Simultaneous tripping of multiple power circuits that are proven not to be interconnected, plus flickering lights on a lighting circuit that is not tripping, suggest to me an intermittent connection upstream, possibly in the DNO supply, as is now suspected.
When an intermittent connection arcs, it causes rapid fluctuations in voltage which momentarily increases the leakage current through interference suppression capacitors connected L-E within class I appliances. These normally pass a small amount of functional leakage current which depends on the supply voltage and frequency. Xc = 1/(2*Π*50*C) and I = V/Xc. But the fast risetime spikes caused by the series arcing subject the capacitors to frequencies much higher than 50Hz, at which their reactance is lower, causing impulses of leakage current sufficient to trip the RCD / RCBO.
So, if the upstream connection arcs, the lights flicker but as there are no L-N suppression capacitors on the lighting circuit, its own RCD / RCBO doesn't trip. But the power circuits are likely to be feeding appliances with suppressors, so these do trip. I bet they wouldn't trip if the appliances were all disconnected and/or if the cooker switch is turned off. Does the cooker circuit feed an induction hob?
Will be interested to hear the resolution.
If I were to guess id say there is a low resitance between both L&N to earth on one of the circuits.. quite often the circuit effected wont trip as the imbalance is shared (both L&N) so the coil on the rcd wont trip.
I can't follow this logic when applied to a 230V single-phase system. You are implying that the leakage L-E is cancelled out by the leakage N-E resulting in no net imbalance, however this is almost impossible for two reasons. Under normal conditions, at most points along the circuit, the voltage between L -E (which is the supply voltage, around 230V) will be approximately in-phase with the voltage between N-E (due to the voltage drop in the neutral conductor, typically a few volts). This means that two similar resistances or reactances, connected L-E and N-E, will pass currents approximately in-phase that add instead of cancelling. There will likely be a slight phase difference between the voltages due to below-unity power-factor in the loads, as the N-E voltage drop is in phase with the load current. But obviously, not so much as to enable cancellation.
We might be able to conjure up a peculiar situation where there is an N-E voltage opposite in phase to the supply voltage, perhaps due to circulating currents in the the earthing system. But even in that peculiar situation we must now also contrive to make the resistances L-E and N-E lie within a specific range of ratios to make the leakage currents cancel. So if there's 230V L-E and say 2V N-E, the resistances must be in the ratio 230/2 to cancel completely. Taking 23mA as a typical threshold for an RCD, a standing leakage of 30mA via 7.7kΩ L-E would need to be cancelled by a leakage N-E of between 7 and 53mA so the resistance N-E would need to lie in the range 38-285Ω
Theoretically possible but most unlikely, so I would tend to discount 'symmetrical' leakage situations on SP+N wiring. Where it is more likely to occur is from conductors with symmetrical voltages. A 3-phase system could leak symmetrically to earth and not trip its RCD, if one were unlucky enough to have three identical low insulation resistances, but that too is pretty unlikely.
