As far as I know, Artex is just a thin layer of plaster applied and shaped onto a solid surface. Plaster is calcium sulphate and does not contain asbestos.

There was a question on Artex removal back in April that mentioned Asbestos in Artex. Part of the answer said "Artex that is more than ten years old will most certainly contain asbestos" for the fuk answer take a look at question 8136 hope this is of some help.