The 44-year-old was driving a white Volkswagen Scirocco and made no attempt to slow down as he deliberately steered towards Victory Gate, the hearing was told.
He smashed through the 80-year-old oak gates on 25 June – shortly before the general election when Rishi Sunak was PM.
Wootten also hit bollards behind the gate and seriously injured himself, the court heard. The damage totalled more than £38,000.
Senior crown prosecutor Celia Mardon said: “CCTV footage showed that Wootten intentionally drove at speed towards the gates of the Chequers estate.
“Not only did Wootten cause significant damage to the Victory Gate, but he could also have put the lives of others at risk with his reckless driving.”
At the time, Thames Valley Police said the driver – who was the only person in the car – had “suffered serious injuries”.
Several cans of alcohol were discovered in Wootten’s car, the Crown Prosecution Service (CPS) said.
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After his arrest, he registered a blood alcohol reading of 221 milligrams of alcohol per 100 millilitres of blood. The legal limit is 80 milligrams.
Wootten, from Great Kimble, Buckinghamshire, pleaded guilty to charges including dangerous driving, drink driving and damaging property being reckless as to whether life is endangered.
He was sentenced on Wednesday to two years and eight months in jail and disqualified from driving for 40 months.
Chequers has been the official country residence of British prime ministers since 1921 and boasts an indoor swimming pool and hundreds of acres of gardens.