I have something I want to tell the Asylum Service in my interview but my family back home could be in trouble if anyone else finds out. Should I say it?

Asylum authorities in all EU countries are required by law not to share information about your application with the people or groups who you say persecuted you. They are not even allowed to tell them that you have made an asylum application. Although they may contact people in your country to ask very general questions to verify your story, they are obliged not to contact your persecutors in any way that might make them understand that you are applying for asylum. This is done to avoid putting your family members back home into any situation that could hurt them or threaten their freedom or security. If there is anything which you are not sure whether you should tell or not, it is a good idea to contact a lawyer or legal counsellor and ask them. Your lawyer or counsellor must also keep any information you tell them secret
Source: EU Common Procedures Directive (2013/32/EC)