I have looked at the original entries of the 1841 census for the Vale of Health, (Woodbine Cottage), and found an ancestor, and numbers of other women living there, to have the annotation FSn (or perhaps PSn) under occupation/disablity. A recent program of "Who do you think you are?" identified similar annotations for inhabitants of Dublin Workhouse, mid C19, as indicating pulmonary disorders, probably tuberculosis.
Is it possible that the sanitorium identified in your article was established as early as 1841 for female TB sufferers from London?