Protesters blocked roads in Liverpool on Friday of last week because a construction firm will not hire blacklisted workers.
Carillion is the main contractor building the Royal Liverpool University Hospital.
It denies blacklisting workers, saying it had “voluntarily stopped” the practice by one of its former subsidiaries in 2004.
The Blacklist Support Group and the Unite union organised the protest.
Roy Bentham of the Blacklist Support Group said Carillion was a “discredited company”.
“The only way they can limit this damage is by giving the workforce pay and conditions in line with national agreements and taking on blacklisted workers now,” he said.
Demonstrators stopped traffic near the hospital but let nurses through.