Contents only insurance or building and contents?

I'm a bit confused over which type of house insurance I need.

I've bought a flat where there is a communal buildings insurance, so it would seem that I need to buy contents only insurance. I understand the concept of contents insurance ie covers everything that would fall out if held upside down, but what would happen with leaks from baths/water tank, electrical damage or fire damage needing complete redecoration, etc?

It would seem these are not covered, but if I bought combined buildings and contents insurance there would be a conflict between insurance companies if there was a claim should the whole building be damaged.

Communal building insurance makes it clear that it does not cover anything inside the flat.