This is a question where you want to be able to show how you worked in a team. It is problematic that you appear to have not worked in a team - as you note, "peer interaction was not existent".
As per your title question,
the answer is to respond with a situation where you showed leadership. This is normally done using "STAR", which is an acronym for how to progress the story.
S. Situation - you begin by describing the situation; "I was selling fruits with my peers when I realised that we were dangerously low on strawberries!"
T. Task - I realised that we were going to need to get more strawberries, and pronto, as the local strawberry eater was due to arrive any minute"
A. Action - I got one peer to buy edible red paint, and another peer to gather our smallest pineapples up, we painted them red and presented them to our strawberry eater as unusually hard and large strawberries.
R. Result - he bought more strawberries than usual! And maybe died! We don't know, but company profits were up that week! Yeehaw!!!
You would, of course, use your own story here - the point is that STAR is the classic method of presentation for soft skills, like a leadership question.
As per your actual question,
you're asking how to present a leadership situation, given you've only ever worked on your own. Leadership is typically thought of as differently from initiative - in our strawberry story above, it is not simply the initiative of selling pineapples as strawberries, but also arranging the peers to take the action and then selling the action that would constitute leadership. Often leadership simply involves getting others to implement someone else's novel idea.
Thus leadership implies that you were working with someone else, and led them. You can hardly lead in a vacuum. So no, you are not showing leadership at all if you've worked on your own.
To answer your question, only the first item, mentoring or training others, really constitutes leadership. The others are examples of initiative.
How do I respond when I've never shown leadership
is probably the real question you're asking. The easiest way here is to think of a time you were led by a peer, and then just turn that story around and say you did it. In the strawberry story, it would be as though you were actually the peer who gathered the pineapples. This is lying, of course, but is the most effective way to give a response.
A better way would be to buy some books on leadership - this HBR book is a really great read. And, having digested that, think about if there is any meeting or group you could form within your company or, failing that, within your industry. This might involve creating a local meetup group for a topic within your industry and arranging meetings - that is an example of leadership.
It doesn't have to be directly work related, and if your job truly offers you no leadership abilities is the best way to gain leadership exposure!