The dispute is between Gleeson MCL and Wates, and centres on claims and counterclaims about failures to complete contracts on time.
Wates' part of the job consists of a £10m contract to install foundations and carry out refurbishment work on retail units above the station. Gleeson MCL, the specialist rail arm of MJ Gleeson, is carrying out £12m worth of work on the ticket office to relieve congestion.
Gleeson is claiming that it was unable to begin work on time because Wates was two months late completing the foundations.
In reply, Wates is alleging that it has been prevented from finishing work on the retail space, being undertaken for client Ropemaker Properties, because Gleeson is six months behind schedule.
A project insider said talks between the parties had broken down. He said time extensions had been agreed, but technical problems had delayed the refurbishment beyond the new deadlines.
He said: "Subcontractors on the Wates project are getting frustrated by the delays because they can't start until a concrete floor has been built as part of the station refurbishment."
He added that all the parties involved were keeping quiet as the dispute was being adjudicated.
A London Underground spokesperson said: "LU has an obligation to provide support to Ropemaker's redevelopment above our congestion-relief project at Knightsbridge station.
"There have been some delays because of the complexity of the two schemes and because of some design changes we have made. But we and our contractors have worked together to reduce the delays."
Wates was unavailable for comment; Gleeson referred all enquiries to LU.