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Not according to this comprehensive list of Storage Heaters Containing Asbestos
Having looked at the list of heaters containing/not containing asbestos I cannot see my heaters listed but I understand that no heaters containing asbestos were sold after 1974. These heaters are in a property that was not built until the mid 1980s so hopefully they do not contain asbestos.
Please let me know if I am correct in thinking this.
As far as I can ascertain, the heaters on the list are the only heaters that contain asbestos... and by process of elimination therefore, yours don't