I'm trying to get the text "Use dropdown if required" and it's price of £0 to stop appearing on emails sent to customers (such as order created etc) if they don't choose a characteristic.
Don't seem to be able to find any option to turn it off.
Well, if that's a possibility of your characteristics, you will see it like you will see the other characteristic's possibilities.
There is no easy way to change that. That would require the edition of code in the file administrator/components/com_hikashop/classes/product.php
The simplest would be to not use a default characteristic possibility in that case.