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The book basically confirms it was Joffrey.
I also don't know how, realistically, it could have been Littlefinger. He wasn't in Winterfell with the king's party. He was still at King's Landing. He couldn't possibly have known that Bran would witness Jaime and Cercei banging it out and then be pushed to the ground and crippled. I think he simply took the opportunity when Catelyn asked him about the knife to further stoke the fires of the Lannister/Stark rivalry by saying that the knife belonged to Tyrion.
A very long time ago, Elio Garcia, the guy who runs the Westeros website and is GRRM's buddy, tried to get around this argument by saying that Littlefinger could have delegated some "sow chaos" authority to a catspaw who then tried to kill Bran. He eventually gave up and acknowledged that Littlefinger not being in Winterfell when it happened was a theory-killer.