Third Party motor insurance is a statutory requirement, and therefore it is right and proper that this information is publicly available.
Household insurance is not a statutory requirement. Public Liability (with the exception of riding schools and nuclear establishments) is not a statutory requirement. Therefore it is nobody's business other than the property owner, or any other person or body who has a financial interest in the property (such as a mortgage company) whether the property is insured, and mortgage companies will generally ensure they are named either as a joint-insured or a co-insured.
As such, and rightly, this information will never be made publicly available.