The clamp looks as if the screw for tightening is the same as the screw for retaining the cable in place.
Admittedly the clamp looks very loose and appears to be held off from the cable sheath by something, however if you were to firmly affix a cable lug (the cable in the picture looks to be larger than the 6mm² you are referencing in the link to the lug you gave) to the clamp then the force applied to clamp the lug will also be applied to tightening the clamp, if the clamp can tighten enough to compress the cores and damage them then they could short to the lead sheath or each other.
That said it does not appear from the picture as if that clamp can tighten beyond a certain point which looks as if it would still be a loose fit on the cable sheath.
A hepworth clamp needs a special tool to close it and uses an earth braid for connection so is not ideal in this case, a constant force spring would be OK but they seem to be hard to obtain easily at a reasonable price.
Since you have had verbal authorisation from the DNO to change the cable it would be worth looking at the job in detail to see what it entails and only proceed once you are sure it is safe and your resulting solution will be secure and effective.