The threat first came to light yesterday when McKeever, who stood as Labour parliamentary candidate for Northampton South last year, tweeted a photograph of a chilling letter he had received.
Addressing McKeever as "comrade" the letter claims he has been "watched" at Portland and states: "Your blood is the price of your treachery."
In an apparent reference to the murdered Labour MP Jo Cox, the letter adds: "Prepare to be coxed."
This comes just days after Len McCluskey, general secretary of Unite, referred to "sinister forces" being behind attempts to remove Corbyn as Labour leader. Repeating claims previously made by a left-wing news website, McCluskey described Portland as "a PR company with strong links to Tony Blair, right-wing MPs, who have been critically involved in this orchestrated coup". Portland dismissed the allegations.
Founded by Tim Allan, a former aide to Tony Blair, Portland includes New Labour figures such as Alastair Campbell among its advisers.
Suggesting that the death threat he received was prompted by rumours of Portland's alleged involvement in plotting the downfall of Corbyn, McKeever tweeted: "Blog linking me to actions of Lab MPs untrue. In interests of safety I'll be saying no more."
Labour peer Lord Kennedy swiftly responded: "@kevinmckeever this is disgusting please report it to the police." Stunned by the news, Francis Ingham, director-general of the PRCA, tweeted: "Incredible. Literally."
By yesterday evening, McKeever confirmed he had reported the matter to the police.
In a posting on Facebook, he said: "Many of you will have read posts on a blog suggesting a link between me, my workplace and the moves by Labour MPs in Parliament. They have no basis in truth."
He added: "I've made my personal views clear on our party's leadership. I have, however, been silent for the past few days due to a hand-delivered death threat, suggesting I should be 'Coxed', a reference to the murder two weeks ago of Labour MP, Jo Cox."
McKeever concluded: "On the advice of the police and in the interests of the personal safety of me and my family, I will not be commenting further."
The posting has prompted numerous messages of support. "I hope the police take this seriously, you should always report any sort of threats or harassment, so I am glad you have. I also think that no one within the Labour family would ever refer to our murdered comrade in such a way, utterly disgusting. Stay safe," wrote Facebook user Chris Spence.
Although most people have been supportive, the depths of the divisions within Labour are highlighted in the views expressed by some responding to the news.
Replying to McKeever’s post on Facebook, Tony O’Malley said: "How can I be sure that your present allegations are not part of the dirty campaign to discredit Jeremy Corbyn and his supporters that has been engaged in by your PR firm? In any event, nobody should deserve personal threats for expressing their views whichever side of the controversy they sit on."
Portland declined to comment.