Britain's biggest unions are warning of a threat of violence by far-right groups during national strike action this month, amid concern that fascist elements are increasingly intent on targeting striking public sector workers.

Unite, Unison and the TUC said they were taking the prospect of disruption by far-right supporters seriously, and had begun to liaise with police to assess any risk to pickets or those on protest marches. The development follows signs that splinter groups from the English Defence League are broadening their campaign from targeting Muslims to trade unionists and socialist organisations. Members of the EDL have recently been involved in attacks on anti-racist and anti-cuts protesters, as well as attempting to target the Occupy movement which has camped outside St Paul's Cathedral.

More than two million workers are expected to walk out on 30 November during a day of protest against public sector pension changes.

Dave Prentis, general secretary of Unison, the country's main public sector trade union, said: "We take any threat to our members' health and safety very seriously. As a matter of course, ahead of a major day of action, we work with the police to assess risks, and our many stewards work hard to keep people safe. The far right's latest attempt to stir up hate and fear is a disgrace."

Rob Johnston, the Midlands regional secretary for the TUC, said: "There is a concern, a general wariness, that the EDL are very active. There have been attacks on trade unionists. We need to put our heads together and think about how we deal with it."

Nine days ago an EDL faction attempted to attack the north-west headquarters of Unite, the UK's biggest trade union. Online messages from the EDL in Merseyside stated they were "patrolling for leftys [sic]". Those they finally identified turned out to be former council workers protesting after they lost their jobs when a contractor went bust. A march of female asylum seekers has also been recently targeted by EDL supporters in the city.

One EDL splinter group, the Infidels, has stated that it considers any leftwing or anti-cuts activists fair game. A north-east wing of the Infidels was recently blamed for attacking an Occupy Newcastle camp in which one protester was taken to hospital and others injured. A statement from the leader of the Infidels faction, John "Snowy" Shaw, states: "We have decided to put all our efforts into opposing everything you do regardless of the issue at hand, it's your organisations we oppose." He adds: "Every event you hold will be a potential target along with your meetings, fund raisers and social events."

On the same day as the Liverpool attack, police arrested 179 EDL members after intelligence they were planning to attack Occupy protesters camped outside St Paul's Cathedral. A Facebook page carried comments discussing attacking "lefties" at St Paul's and included death threats from one supporter.

Dr Matthew Goodwin, extremism expert and political lecturer at the University of Nottingham, said the far right in the UK was becoming increasingly confrontational. "Historically, trade unionists and the far right have been fiercely opposed to one another," he said. "Trade unionists view the modern far right as a continuation of interwar fascism, and so support anti-fascist campaigns and groups. Meanwhile, far-right extremists tend to view trade unionists as promoting multiculturalism and political correctness. While these disputes are ideological, they have often become incredibly personal.

"Over the past three years, the far right in Britain has become increasingly confrontational and provocative."

Bill Adams, TUC regional secretary of Yorkshire, said he was aware of a new far-right presence in his region – 300 members of the North East Infidels recently protested in Leeds city centre – and had been advised by police to avoid antagonising the far right. "They have said to watch what I say about the EDL, they have some info that they have my details." Last year prominent TUC member Alec McFadden was placed under police protection after threats from the Merseyside branch of the EDL who doctored a placard he was carrying criticising coalition cuts to make it read as if it were protesting against homecoming British troops.

Unite general secretary Len McCluskey said the union movement would not be cowed by a group whose only concern was "spreading fear" instead of advancing the rights of working people. "Trade unionists stand against everything the EDL stands for," he said. "Trade unionists have fought long and hard for a fairer society, one with respect at its core. Ultra-rightwing groups care about nothing other than stoking hatred, which is why they have no place in our communities."

Other incidents this year that suggest that the EDL and its spin-offs are adopting an increasingly anti-leftwing agenda include attacks at anti-racist meetings in Brighton and Leeds and during a Labour party event held in Barking, east London, in May.