The firm has told unions that it plans to make 90 redundancies at its Darlington fabrication plant.
And union chiefs at the GMB are now worried that the cuts could spread to site staff as work dries-up in the sector.
Regional officer Jimmy Skivington told the Enquirer: “The firm has a major job on the M74 in Scotland which is coming to an end.
“These redundancies only affect the plant but the two things go hand-in-hand.
“Steel is fabricated at the factory then assembled on site. Less steel being assembled will mean less site work.
“When the M74 job finishes I’m sure Cleveland Bridge will try and find places for its team on other jobs but that can’t be guaranteed.”
The Darlington steelwork contractor employs around 500 workers. It is understood that about 20 workers who have taken voluntary redundancy will leave in July and others in September.
Last year, CBUK won the steel contract for the Shard of Glass skyscraper in London. But the firm had to share the job with rival Severfield Rowen.
It is believed that Severfield is carrying out remedial work to steel fabricated by CBUK on the £350m job where Mace is main contractor.
CBUK fabricated steel for the bottom nine floors and changes are needed following design alterations. The remedial work is expected to take four weeks.
A Mace spokesperson said there have been some minor tolerance issues on the job.
Skivington said: “The firm is now starting to feel the full force of the downturn coming through. There are not so many jobs coming through and CBUK is suffering despite things picking-up in other areas of construction.
“I’ve been around a few years and know these things go in cycles. We will fully consult with the firm and try to get the best result for our members.”