Clove Pink - The herb of Shakespeare
Your photo looks like a very primitive, single carnation, especially the foliage, but I suppose it could be one of the other Dianthus. I can almost smell the spicy fragrance from down here below the border.
a quick internet search of "gillyflower" brings up a Encyclopedia
Britannica article: "any of several scented flowering plants,
especially the carnation, or clove pink (Dianthus caryophyllus), stock
(Matthiola incana), and wallflower (Cheiranthus cheiri). However, the
gillyflower of Chaucer, Spenser, and Shakespeare was the carnation."
your image is specifically that of the pink, though.