13amp is not fine unless you know the current carrying capacity of the cable.
The insulation is not meaningless, that is a very daft thing to say. If it was meaningless you could remove it, but then your cable would go bang as soon as you plugged it in. The outer insulation must pass the relevant safety measures, as this is to protect the user in the event of an earth failure.
You still havent approached insulation resistance.
I'm not trying to pick holes, but i have seen the result of bad/incorrectly installed electrical systems, it can cause loss of property or worse.