Paul Ritchie, 35, targeted more than a dozen different politicians including ex-Commons speaker John Bercow, former Labour leader Jeremy Corbyn, former home secretary Amber Rudd and current Lib Dem leader Ed Davey.
Other victims included former attorney general Dominic Grieve QC, former Liberal Democrat leader Jo Swinson and one-time London mayoral candidate and Cabinet minister Rory Stewart.
Ritchie was traced through two email addresses, including one linked to his business Snapr - a property services booking website - and arrested at his flat in Paddington, central London.
He pleaded guilty last month to 28 counts of sending an electronic communication with intent to cause distress or anxiety over a six-month period between March and August 2019.
On Friday judge Adam Hiddleston jailed Ritchie, of Dolphinton in Lanarkshire, for a year at Southwark Crown Court.
"I have no doubt that you did harbour a deep-seated animosity to those who held opposing views to your own and that appeared to have been your motivation," the judge said.
"The contents of those emails were vile.
"They included threats of violence, such as threats to shoot someone in the face and threats to kill, such as by way of decapitation.
"Those threats were not just directed towards the individuals but also in some case to their families as well.
"Those who received the emails would no doubt be left in fear for their personal safety and that of their loved ones."
The court heard that emails sent to Mr Bercow included references to Jo Cox, who was murdered a week before the Brexit referendum in June 2016.
One email sent to the Liberal Democrat leader Ed Davey read: “If you stop brexit we will kill you and your entire family”, while Mr Stewart was warned: “If you block Brexit... you like likely (sic) be assassinated”.
Plaid Cymru leader Adam Price said he felt “unsettled, upset and concerned for his safety” after receiving an abusive email while having dinner with his family following an appearance to discuss Brexit on the Andrew Marr Show. It warned him “you deserve to get shot in the face you prick”.
In a statement to the court, Commons Speaker Sir Lindsay Hoyle said "the level of abuse, threats and intimidation" received by MPs had increased following the killing.
"Those responsible should face the full force of the law at the appropriate level," he said.
"The members should feel safe in the knowledge they are able to perform their role in democracy."
The court heard Ritchie was suffering with depression and had been abusing drugs and alcohol at the time of the offences.
Emma Fenn, defending, said Ritchie had actually voted Remain in the referendum and felt "genuine remorse and shame at the content of these messages", which "do not bear any resemblance to his political views".
"He is a businessman, an educated man, who is really currently struggling, and who has unravelled," she added.
Additional reporting by Press Association