Dear Sir or Madam,

I'm writing to you today to propose my services as an unpaid intern 
with your organization.

As you can see from my accompanying c.v. I have just finished a degree 
in Economics from the University of Kent. I appreciate that in the 
current job market that I am unlikely to get a paid position if I do 
not have any valid work experience.

This is why I think I could be of big help to your organization. I 
would be happy to work for you for a minimum of 6 months without any 
form of payment. All I ask from you is to give me work experience in a 
variety of areas.

I am somebody that seeks responsibility as I have shown both in the 
university and in vacation jobs that I have had. I am also an 
excellent team  player.  I think I can contribute a lot to your 
organization.

Yours sincerely (truly)