The company was founded in 1591 and specialises in heritage restoration work.
One of its largest current contracts was for Brighton and Hove City Council to refurbish the Dome Corn Exchange and Studio Theatre.
Work on the £21m project has been ongoing since February 2017.
A council statement said: “R Durtnell & Sons Ltd, the contractor working on the major refurbishment of Brighton Dome Corn Exchange and Studio Theatre, has ceased trading.
“We have taken back the site and made it secure. We are committed to completing the refurbishment of these unique buildings to protect their long-term future in the cultural heart of the city.
“Over the coming days we’ll be exploring practical options for continuing and completing these essential restoration works as soon as possible and taking forward the wider Royal Pavilion Estate project.”
Calls to the company’s Kent headquarters were going unanswered on Wednesday and the company’s website and social media feeds were down.
Latest accounts filed at Companies House show R Durtnell made a pre-tax loss of £700,000 from £51.6m turnover in 2017.
During that year the company employed 108 staff.