If someone in England said 'You are not the only one.' it would have been in response to someone who had told him that something had happened, that he agreed with. Is there an Italian who could confirm that this phrase can be used in the same way
Depending on the context, "non sei l'unica" may means "you have a sister" or "your husband has another woman". So, if we don't know the context, "you are not the only one" is a better translation than "you are not alone".
I understand about the definite article but here you're talking about what works as communication and Translating as, you are not unique is perfectly viable in English and is perfectly good communication.