The film does not show Tiberius, who would have died when Boudica was ~7 years old. It does show Emperor Claudius stammering.

http://www.pbs.org/wgbh/masterpiece/warriorqueen/whoswho/claudius.html

http://www.pbs.org/wgbh/masterpiece/warriorqueen/whos_who.html

Haven't seen the movie but you may be thinking of Claudius rather than Tiberius. The conquest of Britain began under Claudius and he was known to speak with a stammer. Suetonius describes him thus:

"his knees were feeble, and failed him in walking, so that his gait was ungainly, both when he assumed state, and when he was taking diversion. He was outrageous in his laughter, and still more so in his wrath, for then he foamed at the mouth, and discharged from his nostrils. He also stammered in his speech, and had a tremulous motion of the head at all times, but particularly when he was engaged in any business, however trifling."

Seutonius, Claudius, XXX