Hi, as you have replaced the MCB, presumably 6A rated, and it is this that trips and not an RCD you do have a serious problem since a 6A type B mcb will carry more than 6A for hours before tripping.
With all lights off there has to be a virtual short circuit some where.
have you had any work done which could have caused cable damage?
eg, hung a picture with a nail through switch wire, screwed down a squeeky floor board, how long ago did this start to happen, gotta be a bit of a detective in this game!
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