Personally,I would never run a 6mm2 cable on a 40A MCB,you have to take into account the heating effect of the extra current.
Normally we fuse our 6mm2 cables at 32A.
32x1.5= 48A
40x1.5= 60A.
We would normally use a 16mm2 cable for a 63A supply(1 Phase), this is regardless of the fact that the installation is protected by BS88 HRC fuses, it is always backed up by an MCB.