The man was employed as a subcontractor on Eric Wright Construction’s £41m college job.
He was taken to Furness General Hospital before being transferred to the Royal Preston.
A spokesman for the main contractor said: “Eric Wright Construction always makes safety at work an absolute priority.
“We are doing all we can to support the family of the injured man.”
Eric Wright said it was co-operating with the Health and Safety Executive’s investigation into the circumstances of the accident, which happened earlier this week.