Why don't you simply ask your consulate (Italian consulate in BA if you plan on marrying in BA) for the "nulla osta"?
From the answer you got, you would need the same document also if marrying as an Argentine national. I don't know how it is called here, it is simply a paper that states that you don't result as married in your country (even if you don't reside anymore in Italy, you are always an Italian citizen).
As for your birth certificate, check with your local office if they are able to issue a multilingual certificate that could allow you to skip to have it translated (for use in the UK).