On his death he left a substantial bequest to establish a charity for the benefit of boys from poor families in and around Derry, which was duly set up in 1840 under the name of Gwyn's Institution.
After William's death Margaret married a man called Andrew McElwaine who had a shop in Bishop Street, Lot 26, in the centre of Derry.
According to a clergyman who knew him he counted every penny, always drove a hard bargain and went out of his way to avoid even the smallest unnecessary expense.,[5][6] Gwyn (with the spelling 'John Gwynne') was recorded as the owner or occupier of the premises in Bishop Street (Lot 26) in surveys of the city dated 1824 and 1826.
Gwyn had experienced the pain of losing his father while still a child, and of being shabbily treated by a stepfather, and this had evidently instilled in him a strong desire to help others who found themselves in a similar situation.
It is on record that he "never rejected the immediate claims of the poor"[11] but at the same time was determined to accumulate enough money to finance a major project for the relief of orphans and other deprived children.
The bulk of his fortune would be used to "feed, clothe and educate" as many as possible of the "male children of the poor or lowest class of society resident in and belonging to the city of Londonderry," preference being given to orphans.
Then ten acres of land were purchased, a park was laid out and a handsome school building in classical style was erected in it, the whole project costing a little under £10,000.
[14] Soon after the opening of Gwyn's Institution Joseph Young, a Derry merchant, bequeathed a large sum for the purpose of clothing, maintaining and educating female children belonging to the City and Liberties of Londonderry.
The moral training of the young was an object that he esteemed to be all important; and his last will proved the sincerity of his desire to promote their welfare, the greater part of his property, all of which had been amassed by his own industry was bequeathed for the establishment and permanent support of a school where orphans boys of all denominations are boarded, educated and apprenticed.