Chris Droogan, Managing Director of Cleveland Bridge UK, blamed the fall on project delays in both its markets.
This meant £15m of UK awards expected in the first quarter of last year failed to materialise until the final quarter, while a large international project was delayed by six months.
Around £14m of 2018 turnover was generated in the UK and £23m overseas.
The revenue drop saw pre-tax profits more than halve to £1.2m in 2018.
There was also a net cash outflow over the year after an overseas client delayed a £5m payment forcing Cleveland to agree fresh bank overdraft facilities, as cash fell from £7m at the start of the year to -£3.7m at 2018 year-end.
Droogan said that Cleveland Bridge had grown its order book in 2019 and expected to once again deliver over £50m of turnover this year.
It also expects to make further investments to improve on its operational costs in 2020 as it delivers its strategic programme of continuous business improvement.
In 2018, Cleveland Bridge also opened an office in Newport to provide sales, design, engineering and project management functions to support projects in Wales and the South West of England.
In addition to its well-established infrastructure business, Cleveland Bridge has also returned to the building structures and bridge services markets, sectors in which the company has previous extensive experience and skills.
The business now employs more than 250 people, including 23 apprentices, and supports a cohort of contractors and local supply chain companies at its 22-acre UK site.