RCD tripping has little to do with "drawing power". There is a leakage to earth (more properly called the CPC, Circuit Protective Conductor) somewhere - and I suspect it's live to earth rather than neutral to earth. If it were Neutral to Earth disconnecting the MCB wouldn't take the problem away.
If you can you should disconnect each MCB on the RCD protected circuits and see if you can identify which circuit is causing the circuit to trip.
However the proper way is to measure the resistance of each circuit to earth. For that it sounds like you need an electrician to do that.