no its 1.5cm any theorys on why it could have happened?
If the cable across its wide dimension is just over 1.5mm as you said, then it's probably 10mm² and OK for the shower. Is the earth core solid or stranded?
If you weren't right with that measurement then it might be 6mm², which could be borderline or even insufficient for the shower. But even so it's unlikely to have got so hot as to melt the insulation.
Which leaves a loose connection as the most likely cause. Have a look at the isolation switch - see if there are any signs of overheating there.
Also if the thermal cutout isn't working, i.e. the shower carries on heating when the water flow drops then you've got another problem to fix. Can't see how that would melt the supply cable, but it's unsafe.
How old is the shower?
is it still ok to connect the wires to new ones making sure that there is no way the wires can touch using insolation tape? if it is ill check it every couple of week to make sure the same thing isnt happning again
1) Insulation tape is no good as insulation - as long as the cables are properly prepared, and have no bare lengths exposed, then it doesn't matter if they touch - that's what their own insulation is for.
2) It would be much better to replace the cable that runs from the switch to the shower than join bits on.
3) The most prudent course of action would be to get an electrician to check the circuit over - make sure it's all OK, make sure there are no hidden faults on the cable etc and repair it. That will probably cost less than replacing the shower if it gets damaged, and certainly less than anything more serious happening....
my idea is to cut the wires just at the back of the shower and extend them about a foot with new wire just wondered what would be the best thing to connect them together with are 30amp terminal blocks ok (the shower is on a ring with a 32amp fuse breaker) or do i need something else to connect them 
