You’re a renter
So it’s up to your landlord to have buildings insurance in case anything happens to the parts of the place they own. The landlord is also responsible for insuring any contents that he owns if the property is rented furnished. If you want to be sure of the safety of your own contents, in the event of anything particularly awful like a fire or a burglary, a contents insurance policy could cover the cost of repairing or replacing your damaged or stolen property.
You're a homeowner
If you own your home and you have a mortgage then it will usually be a condition of the mortgage that you have buildings insurance, but mortgage or not, it’s always wise to have buildings insurance. And contents insurance is just as relevant to you as it is for someone who rents their property
You just own the leasehold
If you live in a flat or a building comprised of different homes on a leasehold ownership, there may be a landlord in charge of the freehold. In this case, it’s up to them to get buildings insurance – but, take note, the landlord is only responsible for the parts of the property they own. So if they look after the stairwell of the block of flats you live in, their buildings insurance will only cover their stairwell. Should anything horrible happen to the part of the property you own it will not be covered by their buildings insurance so you would need to have your own buildings insurance policy.