The student allegedly entered the lecturer's office and tore down an Anti-Nazi League wall poster. The lecturer complained to the university authorities, but no action was taken, according to the lecturers' union Natfhe.
The union has since condemned the university for not taking "decisive action" against the student and says the university failed in its duty of care to provide a safe working environment for the lecturer.
The university is also said to have received a complaint from the student claiming he has been denied freedom of expression. Natfhe has also had reports of comments made in a student's essay saying that he wished more bombs had fallen on London's East End during the Second World War because it was full of Jews and communists.
Natfhe officials said the comments caused offence to the student's lecturer, now retired. The lecturer's personal details also appear on the Redwatch website.
FE Focus was unable to contact him. The lecturer in the poster incident declined to comment for "fear of repercussions".
Last month, Natfhe was told by the university that if she didn't drop her complaint it would investigate the student's counter-complaint through disciplinary procedures.
"We made it clear if that were the case there would be a call for industrial action," said Natfhe's regional spokesman. "We feel the university isn't doing enough to take decisive action and come out firmly against students from the far right espousing their ideology."
The union says further evidence of a BNP presence in the university has appeared through "calling cards" distributed around the library and graffiti in the Stephen Lawrence building.
Following her complaint to the police, the lecturer has asked Greenwich to contact the internet service provider to get her details, including her home address, removed from Redwatch website.
The site accuses both lecturers of teaching from an "avowedly Marxist viewpoint" and "active involvement with the Anti-Nazi League and Socialist Workers' Party".
But a spokeswoman for Greenwich University denied that the institution was at fault.
"If such things had taken place, we would have dealt with them under agreed procedures," she said. "Any sort of behaviour that constitutes harassment would be a very severe breach of our policies. It isn't true to say we have failed in our duty of care."
The spokeswoman refused to comment on whether any student with far-right leanings had been expelled from the university on harassment grounds, but confirmed "isolated" incidents relating to BNP activity, including the appearance of material in the library and graffiti in the Stephen Lawrence building.
A spokesman for Natfhe said the union would monitor the situation and consider applying further pressure on the university if the lecturer's details are not removed from the Redwatch website.
Greenwich University was involved in controversy last year when it emerged that Lawrence Rustem, a politics student and prospective Bexley borough councillor, was a member of the BNP. At the time Doreen Lawrence, mother of race-hate victim Stephen Lawrence, worked at the university. Stephen, 18, was stabbed to death by a gang of white youths at a bus stop in Eltham in 1993.
The Anti-Nazi League demanded Mr Rustem be expelled, but he claimed he had as much right to an education as anyone and should not be victimised for his politics. His details subsequently appeared on the ANL website.
ABUSE ON THE WEB
The website Redwatch refers to Marxists as "unwashed scum" and to the Anti Nazi League as "infantile goons". Its pages contain pictures and details of opponents. It urges supporters to send information about "local red scumbags - we want their names, addresses, phone numbers, photos and work details".
The tone of the Redwatch website is routinely homo-phobic and insulting.
The site purports to retaliate against groups such as the Anti Nazi League which, on its website, depicts BNP parliamentary candidates as "Nazi Scum".
"If the reds remove them, Redwatch will also be removed," the site claims.