At some stage the Artex will have to be removed so that the background can be examined.
The Artex removal will have to be done by asbestos removal specialists.
At the same time the asphalt will also need removing so that the surface of the slab can be examined.
Slab roofs were often installed in the thirties & fifties but Artex only began to be used much later so perhaps the Artex was applied to cover up damage as the slab began to fail?
I work in the Building Trades and I'd hesitate before buying a house with a concrete roof - however, I do understand the desire for a home at a reasonable price.
Usually, it means the property is a fixer-up, and fixing up costs have to be realistically faced - typically, that slab roof has outlived its expected life.