CVU was one of four winners of the eight-year framework in 2013.
It is used by local authorities across the capital in association with Transport for London with an estimated total workload of £2.6bn.
CVU secured the central region with other areas going to Conway/AECOM, Ringway Jacobs and Kier.
The Enquirer understands that both sides decided to part company by mutual consent during a meeting between CVU and TfL earlier this week.
News that CVU could be quitting three years early comes as the Mayor of London and TfL confirmed that cuts in government funding would mean a hiatus on non essential road repairs.
The mayor’s office said: “All non-essential road improvements have been paused for two years unless suitable funding can be found.
“So while TfL will ensure roads are kept safe, this lack of proactive work could lead to an increase in disruption on the roads with increased closures and speed, size and weight restrictions.”