In a High Court writ, Skanska is claiming for an extension of time to finish works at the site, as well as money due under a subcontract made in October 1999.
Skanska is also seeking damages for direct loss and expense, release of retention and interest for the late payment. The total amount of the claim is £5,029,742.25. Both Skanska and Costain refused to comment.
Building first revealed that the £46m hotel refurbishment project had hit problems in December 2001 after it emerged that it was one of the loss-making contracts that have dogged Costain and Skanska joint ventures.
The handover of the hotel, now the Hilton London Paddington, to client Muirgold in January 2002 was more than a year late.
At the time of the refurbishment's initial problems, one project source said that it had been a "highly complicated" job.
One reason for the difficulties was that the project was next to a railway station and many safety issues had arisen.
A source close to the scheme also said that management changes had concerned the client. He said: "The scheme has had four project managers during its history." The source added, however, that the quality of the project had not been a problem. He said: "The quality is first class. That has been the great attribute of Costain and Skanska – they have never let the quality drop."
The Paddington hotel was the latest in a string of declared losses on a number of Skanska and Costain projects, which have not been named.
Skanska bought a 7.6% stake in Costain in 1997, before selling it in November 2000. The two firms have worked on other schemes such as a £70m shopping centre in Uxbridge, west London, and a £30m development at Northgate House in Hackney, east London.