Old Royal Naval College.

Health Before it reopened as the college, the building was originally developed to house the Greenwich Hospital for seaman. British History Online has a lengthy history of the hospital reproduced from the book, Old and New London, published at about the time the change of use happened. It's admittedly pretty arcane but there are some wonderful details:

"The hospital, as we have seen, was first opened as an asylum in 1705, when forty-two disabled seamen were admitted. In 1738 the number of pensioners had increased to 1,000, which had become doubled in the course of the next forty years. The number was subsequently increased to about 3,000, independently of about 32,000 out-pensioners. Each of the pensioners had a weekly allowance of seven loaves, weighing 1 lb. each, 3 lbs. of beef, 2 lbs. of mutton, a pint of pease, 1¼ lb. of cheese, 2 oz. of butter, 14 qrts. of beer, and one shilling a week tobacco money; besides which he received, once in two years, a suit of blue clothes, a hat, three pairs of stockings, two pairs of shoes, five neck-cloths, three shirts, and two nightcaps."