While it is a good story and it definitely shows perseverance and other valuable skills, I believe it is a bit of a stretch for "leadership". An admissions committee wants to see how you act when leading others (peers or those junior or senior, but, other people must be involved!). It could be leading a large team or leading one other, but, I think it is almost impossible to write a good leadership essay if it doesn't involve any interactions with others.

HOWEVER, with that said, you could absolutely still use your Barclays job search example as a support. For instance, perhaps there is another leadership situation in your life in which you decided to gain more knowledge and improve your skills rather than act hastily or out of fear - maybe you learned to have confidence in yourself and your (eventual) ability to reach your goals because of what you went through with your job search. Maybe being faced with the adversity (recession type environment) made you more willing to work hard as a leader in another situation, etc. Obviously, I don't know what other example you want to use, but, I'm just trying to give a broad example of how you might be able to incorporate the story successfully.

And, don't worry about it being a purely work related story. The leadership experience doesn't necessarily have to have been successful - you can write a good essay about a less than perfect leadership time as long as you write about what you have learned since and how you would be more effective as a leader today.

I hate to send you back to the drawing board, but, I'd try to rework this answer! Hope this helps.

Best of luck to you!