It can be a bit confusing when talking about water damage and contents insurance so let's break it down.

The general rule is you're covered if a pipe bursts or water leaks from an external pipe and damages your belongings.

If the pipe is internal or damages only the fixed parts of the building, then that's usually covered by building insurance.

An external pipe is one that you can easily see and isn't normally hidden behind a wall or panelling to get to it. For example, the pipes of your radiators, the pipes under your kitchen sink, the pipe from the washing machine and toilet to the main source, would all be considered external.

An internal pipe would be one that you can't see as it's under the floor, within the walls or behind some panelling where it's not easily accessible. For example, pipes and plumbing to a bathtub and shower are generally behind panels or tiles.

The next thing to bear in mind is that there has to be a leak, which is defined as "water that has improperly flowed out of water supply pipes or equipment connected to the pipes", so dropping your phone in the sink or toilet would not be covered.
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And last thing to remember is that the coverage is to your personal belongings and not the fixed components of the building. If the radiator leaks and damages your rug, that would be covered, but the damage to the floor under the rug would be covered by your landlord's building insurance.*

This is where things can get tricky! The rule is that the first habitable floor of the property is always covered by building insurance regardless of who purchased and installed it.
For example, you move into a place with vinyl flooring and you lay some nice parquet over it, damage to your parquet would be covered by household contents.
If the floor you install is directly on the concrete, that hasn't been sealed and polished to a habitable state, then any damage to your floor would be a building insurance claim.