What are my walls made of?

[UnderHisEyeBall]

We spent today on attempt no. 2 of putting up an Ikea Lack shelf in the bedroom.

It is incredibly hard to drill into the wall. There are no studs. We checked with a stud finder that found studs on other walls in the house, but not on this one. We assumed it was brick as though it is an interior wall it is extended from an external brick corner wall (difficult to explain). However, when we drill in with a masonry bit, we go through about 2 inches of plaster and there is no brick dust coming out. Just pale, plaster-type dust.

But plaster would be softer wouldn't it? Is it a concrete wall?

For background the house is 60s and the walls are in pretty good/almost perfect nick throughout. It was one of the reasons we bought the place. There is a local rumour some other nearby 50s houses' internal walls were rendered with cement, but this is a different development.

Cement render is tougher than plaster but that's generally used on the ground floor of houses because it's better for damp. It sounds like your wall is some kind of tough concrete, or it could just a lintel where a wall was previously filled in. Another option is just you hit something eg metal capping or a redundant pipe.