If you are a tenant you should protect your own belongings in your rented house by taking out an appropriate insurance policy.
Your landlord should insure the building, fixtures and fittings and any contents (e.g. furniture left in the property), as a tenant you are responsible for insuring your own possessions. You should check with your landlord that they have insurance before signing your contract, it is normally a condition of the contract that they do. If they do not have insurance you should carefully consider how this would affect you should something happen e.g. a major fire.
It is illegal for anyone to advise or sell insurance unless they are regulated by the FSA and you should check with the FSA (The Financial Services Authority www.fsa.gov.uk) if you are in any doubt.