Coupons and Shipping

Product value of £6
Coupon worth £10
Shipping £3

Total order value at checkout = £0.
Should it be £3 - i.e. the shipping value?

Indeed. It seems more logical to keep the shipping fee. Please try to add the lines:
if(bccomp($cart->full_total->prices[0]->price_value_with_tax,0,5)<=0){
$cart->full_total->prices[0]->price_value_with_tax = 0;
$cart->full_total->prices[0]->price_value = 0;
}

in the file administrator/components/com_hikashop/classes/cart.php just before:
$shipping_id = $app->getUserState( HIKASHOP_COMPONENT.'.shipping_id');

Works great thanks - another one for next release please.

Yes.