In the middle of his anatomy lesson, Schoolmaster Dr Alexander Smart receives a letter regarding his application for the position of Headmaster at Narkover School. To help him secure the job he must obtain a reference from the Governor of Blackstone Prison, where he conducts a weekly lecture. On the day of his lecture, the Governor, with Smart's unwanted assistance, dictates a glowing reference to the prison trustee Faker Brown.

That very day Brown is released from prison and arrives at Smart's lodgings with the Governor's reference. He steams open the envelope and reveals to Smart that the Governor dictated a different letter with no recommendation. Brown has the original unsigned reference in his possession and demonstrates the art of penmanship with a perfect forgery of the Governor's signature. Brown posts the fraudulent letter to Narkover.

Smart arrives at Narkover to a traditional welcome - a bomb under his taxi, then dragged along the road for an involuntary ride on a carpet. The schoolboys carry him shoulder high into the school grounds and give him a ceremonial blanket tossing until he is left hanging by the seat of his trousers over the school doors. He plummets to the ground in time to be greeted by Lady Dorking and the school board. Missing from the welcoming party is Colonel Crableigh, the school's vice-chairman. He opposes Smart's appointment and intends to discredit Smart and appoint his nephew, Mr Finch, the current vice-headmaster, as the new headmaster.

Smart has his watch stolen and loses his money playing cards with the sixth form boys. The boys scarper when they see Crableigh, leaving Smart caught red handed. Unaware who he is addressing, Smart tells Crableigh to mind his own business. He gets his own back on his students by playing them at their own game: cheating.

Crableigh demands Lady Dorking sack Dr Smart, but the Headmaster charms Lady Dorking onto his side with a card trick. Faker Brown, visiting his son Cyril, spots Lady Dorking's jewellery and, so that he can keep an eye on it, blackmails Smart into finding him a position as a school porter.

On the morning of the school's Founders Day, Smart takes a Geography lesson. He is pelted with ink pellets and mocked. On the door of his study has been chalked with 'Smart Alec is a Gump'. He convinces Lady Dorking that it means 'a friend in need'. The flirtatious Lady Dorking hints to Dr Smart that he could be her gump. He amuses her with a conjuring trick involving her watch. Lady Dorking performs the same trick using Crableigh's watch, with disastrous results. Spotting Lady Dorking's necklace on the floor, Crableigh hides it in the Headmaster's pocket. After much to-ing and fro-ing between Smart, Crableigh and Faker the necklace ends up resting in Smart's desk drawer. To get the necklace back to Lady Dorking without arousing suspicion, he hides it in a jewellery case to be presented to her by the school at the Founders Day luncheon.

After a hearty lunch and a rousing rendition of the school song, Cyril presents Lady Dorking with her jewellery case. He has picked the lock and stuffed the necklace into the rugby ball for the Founders Day match between the Old Narkovians, captained by Faker's brother, and the current scholars, led by Dr Smart.

The match commences and, in the middle of a scrum, Smart learns the whereabouts of the necklace. A fight over the ball leaves Mr Finch, the referee, knocked out cold and Smart swallowing the whistle. The offending item is dislodged as the boys turn him upside down. The ball makes its way to Smart and he drop kicks it into the waiting arms of the police. He informs them of its contents. Crableigh attempts to frame Smart but Faker stands up for Smart and explains the real events. A fight breaks out.

The triumphant Smart is carried off the pitch shoulder high by his scholars. They throw him into a blanket and toss him repeatedly into the air.