To be absolutely certain only by getting an asbestos analyst to take a sample and analyse it under the microscope. At worst it is not going to contain more than 2% asbestos fibre. Most Artex and similar materials manufactured after about 1985 don't contain any asbestos; some companies stopped using it before - but who knows how long it had been sitting around before people mixed it up and slapped it on.
Was in B&Q once when a member of their staff advised a member of public to use a belt sander to remove it rather than the angle grinder he was thinking of.
Best way to deal with Artex is to overboard the ceiling and skim over the new plasterboard - done well you should only lose a cm or two of ceiling height.
The analyst must be accredited under the UKAS scheme - good though Boots might be for some things - asbestos analysis isnt one of them. Yellow Pages should help - there are plenty of such labs around.
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