Dann,

If your grandfather naturalized in the UK before your father was born, he renounced his Italian citizenship and could not pass it to your father. Dual citizenship was not permitted until 1992.

However, as a citizen of the EU, you technically don't need Italian citizenship to live and work ...

From the information you've provided, it does not seem you qualify. However, you can obtain citizenship after residing for three years in Italy (this is because you can document an Italian heritage).

I understand your strong desire to do this--and don't worry about U.S. citizenship; you won't lose ...

It's not the petition of naturalization they are interested in--only the actual naturalization so you would qualify on that basis. However, because you are claiming citizenship through your mother/grandmother, your mother must have been born AFTER 1948 or your grandmother could not have passed ...