Eight large construction firms have announced that they intend to compensate workers who were unlawfully blacklisted and denied work for long periods.

The firms have also apologised to the workers whose names were stored in a secret database.

The move follows years of campaigning by the workers, who said they were often barred from working for raising legitimate concerns about health and safety on building sites. Many say their lives were devastated as they were prevented from getting jobs for years.

More than 40 firms in the construction industry funded a clandestine agency that kept files on more than 3,200 workers that they deemed to be politically disruptive. The blacklisting agency operated for 15 years until it was raided and closed down by a watchdog in 2009.

No details of the scheme were disclosed by the eight construction firms on Thursday. The companies – Balfour Beatty, Carillion, Costain, Kier, Laing O'Rourke, Sir Robert McAlpine, Skanska UK and Vinci – said: "The scheme is intended to make it as simple as possible for any worker with a legitimate claim to access compensation."

Representatives of the blacklisted workers gave the announcement a sceptical welcome, saying: "Forgive us if we do not crack open the champagne just yet … So far there are no firm proposals, only a vague promise of compensation for any workers with a 'legitimate claim'.

"This is a cynical move intended to reduce corporate reputational damage. We do not for one second believe that these companies have suddenly seen the light. Most of the senior managers implicated in the blacklisting conspiracy are still in post. The only thing they regret is being caught."

The workers have said they intend to continue their legal claim at the high court on 29 November for compensation for being blacklisted, as well as their campaign for a public inquiry "to expose everyone involved in this human rights conspiracy".

The eight firms announced their apology for funding the blacklist and "the impact that its database may have had on any individual construction worker".

They said they had invited representatives of the blacklisted workers to talk to them to "ensure that the proposed terms of the scheme are fair and effective".

They encouraged other firms that had funded the blacklist, disguised under the anodyne name of the Consulting Association and run from a nondescript office in Droitwich, Worcestershire, to join the scheme.

Justin Bowden of the GMB trade union said: "Firms admitting they engaged in a terrible abuse of the civil rights of thousands of UK workers is an important step."

The Unite assistant general secretary Gail Cartmail said: "Many of these workers have spent years out of work as a result of being blacklisted. Employers have a moral duty to give them back the jobs that were wrongly taken away from them."

The workers also want a public inquiry to examine their claims that police secretly gathered intelligence on some of them and passed the information to the blacklisters.

In August, the Guardian published testimony from Peter Francis, the former undercover officer who has become a whistleblower, who said he believes that he personally collected some of the intelligence that later appeared in the blacklisting files.

Managers in the construction industry pooled data about individuals to maintain the secret files. When the workers applied for work, the managers would contact the association to check the entry on the potential employee and then decide whether to give them work.

The files, which contained information dating back to the 1980s, contained descriptions such as "militant ringleader", "agitator", "is a good worker but has proved to be very militant", "do not touch", and "that subject is a very bad troublemaker and would not be re-employed".