Do the charging cables really fall outside any testing requirements?

As I recall, the Electricity at work regs don't specifically demand testing at all - but simply demand duty holders ensure that all systems are kept in a safe condition - periodic testing is just one (if very common) way of demonstrating that the requirement has been achieved. So the statement is possibly technically correct, even if likely to be misleading without a fuller context.

   - Andy.

Is it because vehicles come under Construction & Use regulations?

I can believe a 15% loss from mains going in, to DC power coming out of the battery.  The process isn't going to be 100% efficient.

This appears to apply to the low power AC charging cables with a connector at both ends. For a private user it will probably just be abused  until it fails, for a business user there probably should be some form of risk assessment. How great is the risk if a live conductor becomes exposed? As I understand it all the likely sockets the cable could be plugged into will have RCD protection. What will happed if a live conductor starts to break giving a high resistance 'hot spot'?

The higher power charging cable that are fixed to the charger hopefully have some sort of testing routine. 1000V 500A capable systems are in use and 1MW systems are in development, but these should have suficient internal monitoring to minimise the risks.