Some of Corbyn's advisors were ex-Trotskyists and communist sympathisers
Advisors to Jeremy Corbyn are ex-members of Trotskyist organisations from the 1980s.
According to Dame Stella Rimington, they were investigated by MI5 for “subversion”.
Some of them are now members of Momentum, the left-wing grassroots organisation that helped create support for Jeremy Corbyn’s leadership bid.
Dame Stella at the Cheltenham Literature Festival, said: “I now see in Momentum some of the people we were looking at in the Trotskyist organisation of the 1980s, now grown up and advising our would-be prime minister Mr Corbyn on how to prepare himself for power.
"Looking at it from the outside now that's quite an ironic turn of events."
When asked if she could remember any names she added: "Certainly their names are familiar, shall we say that much?”
Chief of staff of the Unite union and former member Andrew Murray was a former member of the Communist Party of Britain and was at the Labour HQ in the run-up to the General Election.
Unite is also Labour’s biggest donor.
Mr Murray left the Communist Party last year to join the Labour Party.
Momentum’s organiser in Haringey, north London, Liam McNulty was also an activist in the Trotskyist Alliance for Worker’s Liberty.
Dame Stella, 82, worked for MI5 from 1969 until 1996.
Her work involved compiling lists of members of “subversive organisations” which would be consulted as part of a vetting process if anyone applied for a job that could grant them access to secret information.
Dame Stella said: “Under Clement Attlee came in the rule that nobody who belonged to a subversive organisation should work with access to sensitive information, secret information, classified information.
"The only way one could ensure that that operated was by knowing who the members were.
"So our job was to find out exactly who the members of the Communist Party of Great Britain were and various subversive organisations identified as wishing to destroy the democratic system of this country.”
General Election 2017: the most shocking election in recent history
Thu, June 8, 2017
No-one saw it coming. A resurgent Labour has delivered a humiliating blow to Theresa May. While still the Prime Minister, the Conservative majority has been decimated
Reuters/PA/./EPA 1 of 39
How has the election panned out for the four main parties?
When asked if the groups posed a genuine risk, she said: “Their plan was that they didn't believe in the democratic system.
"If you went to the Communist Party of Great Britain headquarters, where they were being directed by members of the Soviet communist party and receiving sums of money to do various things that obliged the Soviet Union, that's where you have to look at it.
"If a member of the Communist Party of Great Britain had got access to secret information then there might have been a problem because they might then have been of interest to various people in the leadership and might well have passed things on."
This year it was revealed that Jeremy Corbyn was investigated by MI5 for his links with the IRA.
A source close to the investigation of Mr Corbyn told the Telegraph MI5 had officially opened a file on the current Labour leader by the early 1990’s.
Dame Stella Rimington worked for MI5 from 1969 until 1996
It was claimed last year the Metropolitan Police’s Special Branch was also looking at the then backbench MP – although it is unclear if their investigation was linked with MI5.
A spokesman for Mr Corbyn said: "It is well documented that a wide range of trade union and political activists, including future senior government ministers, were monitored in the 1980s by the security services.
"It would be a breach of the Official Secrets Act and of her obligations as a former senior MI5 officer if Dame Stella Rimington divulged privileged information."
A Momentum spokesman said: "Nameless allegations harm our political debate, and we'd recommend Stella Rimington refrain from making them in the future."
New Labour also had many ex-Trotskyists within the party ranks.
Tony Blair admits that he was a "Trot" while at university
John Reid, David Triesman, Peter Mandelson and Charlie Whelan were front bench MPs and also ex-members of the Communist Party of Great Britain.
Stephen Byers and Alan Milburn were connected with sub-Marxist organisations in the 1970s.
David Triesman is a former trade union leader and was a significant figure of the Euro-communist movement of the 1970s.
Even Tony Blair, who is often called a “red Tory”, admits he was a "Trot" while at university at Oxford in the 1970s.
He told BBC Radio 4's Reflections: ”When I got back I picked it up and started to read it. And I literally didn't stop reading it all night. It opened a different world to me.
"I suddenly thought the world's full of these extraordinary causes and injustices and here's this guy Trotsky who was so inspired by all of this that he went out to create a Russian revolution and change the world.
”It was like a light going on.”