Apparently the movie and book represent alternate realities, because this never happened in the book. However, if it would have happened in the book, we can venture a guess that Snape would have been the previous student.
Later in the book (Chapter Fifteen), Slughorn discusses Harry's Potions ability with other teachers, and he mentions the amazing Draught of Living Death that Harry concocted (my emphasis):
"But I don't think I've ever known such a natural at Potions!" said Slughorn, regarding Harry with a fond, if bloodshot, eye. "Instinctive, you know — like his mother! I've only ever taught a few with this kind of ability, I can tell you that, Sybill — why even Severus —" And to Harry's horror, Slughorn threw out an arm and seemed to scoop Snape out of thin air toward them. "Stop skulking and come and join us, Severus!" hiccuped Slughorn happily. "I was just talking about Harry's exceptional potion-making! Some credit must go to you, of course, you taught him for five years!"
Trapped, with Slughorn's arm around his shoulders, Snape looked down his hooked nose at Harry, his black eyes narrowed. "Funny, I never had the impression that I managed to teach Potter anything at all."
"Well, then, it's natural ability!" shouted Slughorn. "You should have seen what he gave me, first lesson, Draught of Living Death — never had a student produce finer on a first attempt, I don't think even you, Severus —"
In the first paragraph he implies that Snape was the best at Potions prior to Harry. In the last paragraph he implies that Snape's attempt at the Draught of Living Death was the next best after Harry's.
If there had truly only been one previous student to brew one sufficiently worthy of the prize it would then stand to reason that this student was Snape.
Of course, this is not ironclad evidence as it is possible that Slughorn used Snape as the example because Snape was there, even if there may have been one or two students that were better than him.