Is Emotional Intelligence (EQ) a pre-requisite for all leadership positions and to what extent can one exercise this skill within any work setting?

I think a person wth a high EQ is quite the advantage for any company because such a person has better creativity , brainstorming and adaptation skills . This person can deal better with change and can separate his/her professional life from his/ her personal life . professionalism gets better and quicker than most employees.

Nobody can really agree whether EQ is a real thing, and if it is a real thing what kind of real thing it is, so it's usefulness in any context is questionable.  However, if you mean the ability to interpret correctly the emotions that other people have or are likely to have, and the further ability to respond to those emotions in a way that the person feeling them finds helpful, then yes, this is a useful skill for any leader to have. 

It is not a prerequisite - being a good leader involves a balanced portfolio of skills and attributes which interact with each other, so you can't really say that any single one of them is a prerequisite.

Note that EQ is like anything else - some is good, too much is bad.  You cannot be a good leader if the emotions of people in your team gain too much importance.  A good leader sometimes has to make hard decisions quickly, which will make people feel bad. People with very high EQ can find that difficult or impossible.

No, it does not qualify as a pre requisit