I took a look at the Fitzwilliam Virginal Book, because it sounded like some of the pieces from there. The only Toccata I found was by Giovanni Pichi, but was in d minor, not your piece which is in g minor. It does sound Italian, however.
All the other possibilities in FVB are labeled Preludium. It would take some time to go through all of them, and anyway your piece is clearly marked Toccata. I would suggest looking at Italians from the late 1500's, early 1600s. Merulo, Gabrieli?
Or maybe Bull or other Elizabethans or maybe Dutch? Italian is my guess. It could even be an improvisation "in the style of".
Good luck. It would probably take less time to notate the piece in dictation than to hunt for it!
RS