Yes, check the terms of the lease, but 99% of residential leases will state that it is the Landlord's obligation to insure the building. And in any event you cant insure something that you have no insurable interest in. So if you dont owe it you cant insure it.
One thing to check is that the lease has a cessation of rent clause, so if the building is no longer habitable from a fire or flood you are no longerrequired to pay rent.
Er, I think you're confusing leasehold title and an occupational lease/shorthold tenancy. If the house isn't habitable the tenant doesn't have to pay rent, no matter what the tenancy agreement says - habitability is both a fundamental term of the contract and a statutory requirement under the Housing Acts.
You only need contents insurance for
your contents, Mr Paul. If the landlord wants cover for fittings/appliances which go with the house, he has to arrange it. And don't automatically pay to insure your own stuff - I haven't bothered for twenty years and even with a couple of minor burglaries I am well on the winning side.
{NB Mr Paul. If your contents are damaged by something which the landlord should insure or has insured for e.g. a burst pipe, you are only going to be able to claim from the landlord or his insurers if he has actually been negligent. It isn't enough that an event for which he is responsible has damaged your goods.]