When is a car Used or New

I purchased a car from a dealership on 11th July which was first registered on 20th June.
On some documentation it is described as Used whereas on others it is described as New.
When is it classed as Used?
Furthermore, the dealership invoiced me almost £500 delivery fee when I picked it up from them and claimed that I had to pay it as I was the first owner.
Surely they were the first owners as they registered & taxed it in June?

Any clarification would be welcome!