Should house insured by landlord

Have you read your tenancy contract? It almost certainly requires you to take out insurance including fire cover (although insuring your own contents is a matter for you to decide, but they certainly won't be covered by the landlord's insurance).

As a landlord, you need landlord's insurance. As a tenant, you need tenant's insurance. Given that in either case you're going to need to talk to an insurance broker, go and see one and get some proper advice.

Q - Could anybody give some advice?
A - Go to your bank, or any insurance company or insurance broker and get tenants insurance.

it's a tenants duty - look in your rental contract! same as to perform the annual heating control !