Normally, when the panel is working, it means Residual Current Circuit Breaker (a type of GFCI) can be in the on stage, but while checking the current between neutral and ground the RCCB is getting tripped. Can anybody please explain why this happens?
This is normal. There can be a slight potential difference between the neutral and ground at a receptacle. (This would be due to a load on the circuit.) If you provide a current path to ground, then current will flow in the neutral path and there would be no corresponding current in the hot. A difference in the current between the neutral and the hot will cause the RCB (GFCI in the US) to trip.
EDIT Another way to look at it is that connecting the neutral and the ground at a receptacle divides any current flowing in the neutral path thereby reducing its value below that flowing in the hot path. This causes a difference in the current flowing in the hot and neutral paths. This will trip a RCB if it is in the receptacle or in the circuit breaker for the circuit or the master breaker.
EDIT2 There has to be enough current flowing through the RCB for a connection between neutral and ground to trip the RCB, that is, the circuit must have a load somewhere causing current to flow through the RCB.
If a circuit is completely unloaded and a low resistance path is established between the neutral and the ground (such as a connection with an ammeter), then the RCB would not trip.
In the case of RCB receptacles they can be in a loaded circuit, but on spur (as they would be if they are connected by pigtailing) or they can be "distal to" (beyond) the location where the neutral and ground are connected. I think the RCB receptacles would trip in those cases, but I doubt this is relevant to the OP's question here. He is probably asking about an RCB breaker.
Working as intended. A neutral-ground fault is still a ground fault.
In fact, some US GFCIs actively check for this during their power-up self test.
GFCI/RCD isn't about voltage, it's about leakage. Leakage on neutral can be just as deadly when combined with another problem.
Also, I'm not quite sure why you're checking for current between neutral and ground, since the RCD already does that. Literally, the RCD compares current on the hot to current on the neutral, and they should be equal. If they are not equal, it trips. The RCD does not examine or interact with ground at all, but I cannot imagine a way for there to be any neutral-ground current and yet have the hot current and neutral current still be equal.