Jonathan Chew, 24, approached him as he walked through St James’s Park in Westminster on 27 June last year.
He filmed England’s chief medical officer on his phone.
Footage of the incident, lasting around 20 seconds and showing Chew alongside former estate agent Lewis Hughes, was widely shared on social media.
The court was told Chew, who vaped and sang during the hearing, had learning difficulties
Appearing at Westminster Magistrates’ Court on Thursday, Chew, of Chelmsford, Essex, admitted a charge of intent to cause harassment, alarm or distress to Sir Chris.
He also admitted obstructing Pc Steven Ozden.
‘He didn’t choose to be in the public eye’
District judge Paul Goldspring jailed Chew for eight weeks and ordered him to pay £1,058 in costs and compensation.
He said: “You chose at that point to make a very conscious decision, I have no doubt in an effort to avoid being prosecuted for your offending.
“Unfortunately that wasn’t something you put right immediately.”
Mr Goldspring added that Sir Chris has responded to “an unprecedented crisis over the last few years” with “great dignity” and “great professionalism”.
“He didn’t choose to be in the public eye. He is entitled to go about his work. He is entitled to go about his daily life,” Mr Goldspring added.
“You targeted him, in the sense that you recognised him from the TV,” he said.
“Although you did not upload the video, you were complicit in sharing it.”
“You had a significant, I go as far as to say, an appalling criminal record,” he added.
Mr Goldspring said he also wanted to create a “deterrent” to stop people accosting those who do not choose to be in the public eye.
The district justice said he gave Chew “full credit” for pleading guilty at the first opportunity to the charge of intent to cause harassment, alarm or distress.
He also said he accepted Chew did not initially intend to be hostile and suffered from learning difficulties, mental health issues and autism.
Chew was asked to stop vaping during hearing
As he was sentencing Chew, Mr Goldspring interrupted proceedings to ask him to stop vaping.
Chew also responded to the costs announcement by saying: “That’s peanuts.”
”Your contempt for these proceedings and this court have been breathtaking throughout the process,” Mr Goldspring said.
But as Chew was lead out of the dock, he began to sing “West Ham ’til I die” loudly.
During the hearing, prosecutor Iestyn Morgan said that Chew started filming Sir Chris on his phone while Hughes grabbed him in a headlock.
In the footage, shown to the court, the pair can be seen jeering as Sir Chris attempted to break free.
The court then heard how Chew gave the name and old address of his brother to the police officer.
Mr Morgan said: “This did cause a waste of police resources.”
He said police attended the address on 1 July to discover a man called Harry now lived at the address.
Officers were then able to identify that Jonathan Chew was the suspect after he provided comments about the incident to The Sun newspaper.
The prosecutor added that Sir Chris suffered “the added humiliation of the recording being forwarded and uploaded”.
Rabah Kherbane, defending, argued that Chew had learning difficulties, “intellectual difficulties” and “delayed maturity” and often becomes “frustrated” when trying to communicate with others.
Hughes, 24, of Romford in Essex, earlier pleaded guilty to a charge of assault by beating and was sentenced last July.
He was handed an eight-week prison sentence, suspended for two years, and was ordered to pay a total of £307 in fines and compensation.
He was labelled “yobbish” by the Mr Goldspring and was criticised for leaving Sir Chris “humiliated” after putting him in a headlock.
Chew was handed an eight-week custodial sentence for intent to cause harassment, alarm and distress and two weeks for wilful obstruction of a police officer to run concurrently.
He was also ordered to pay £1,058 in costs and compensation.
A message from the editor:
Thank you for reading. NationalWorld is a new national news brand, produced by a team of journalists, editors, video producers and designers who live and work across the UK. Find out more about who’s who in the team, and our editorial values. We want to start a community among our readers, so please follow us on Facebook, Twitter and Instagram, and keep the conversation going. You can also sign up to our email newsletters and get a curated selection of our best reads to your inbox every day.