What the landlord's policy covers
The owner of the flat insures the property: the walls, the built-in fittings, the building. That policy exists to protect the owner's asset, not the tenant's life inside it.
Two things stay outside it. Your belongings - furniture you brought, a laptop, a bicycle, clothes. And the damage you cause: to the flat itself, to the flat below, to a person.
The two policies that close the gap
Household contents insurance covers what is inside the flat and belongs to you. It matters more than people assume - add up a laptop, a phone, a bike and a wardrobe and the figure is rarely small.
Personal liability insurance covers damage you cause to somebody else. This is the one that saves people. A hose on the washing machine gives way while you are at work; by the evening the flat below has a ruined ceiling and the repair bill runs into six figures. Without liability cover, that is your money.
What to check
Look at the sum insured for contents - it should reflect what you actually own, not a round number picked at random. For liability, look at the limit: injury claims are the expensive ones and the difference in premium between a modest and a high limit is usually small.
Then read what the tenancy agreement requires. Some agreements oblige the tenant to hold liability insurance, and a few specify a minimum limit.