If you’re a tenant, your landlord is responsible for taking out buildings insurance. It’s still important to check they’ve got this covered when you sign the tenancy agreement and you should not be afraid to ask for proof. We have all witnessed buildings collapse and People’s buildings being broken into.
Contents insurance for your personal possessions is down to you though. Cover for the landlord’s contents, like the sofa sets if they rent the property part-furnished, is their responsibility.