If you and your ex-partner were not married, what the impact will be in custody proceedings will depend on whether both of you have established Parental Responsibility. If both parents have Parental Responsibility, the fact you were not married should make no difference to custody proceedings.
However, if one parent did not have Parental Responsibility, this means they will have no automatic legal right to custody, access or contact with their children. In such cases, gaining Parental Responsibility will therefore be an important first step in deciding custody for your children.