A spokesperson for CPC confirmed that the firm was no longer employed as construction manager, but said it was still acting as project manager.
He said: "The [construction management] contract has been rescinded, and all options are currently being considered. It's an unprecedented situation in our experience."
Anthony Thorp, a director at Thorstone Land & Property, which is acting for developer Lion Heart Properties, said CPC would remain on site until the end of November.
He said: "We have deadlines that need to be met and so we've got an in-house team that will complete the project in the next couple of months."
Thorp refused to be drawn on why CPC had been released from the project, but did say that the change in construction managers would not affect the cost of Lion Plaza, and that he expected work to finish by the end of February.
The 22,225 m2 mixed-use scheme lies at the apex of Threadneedle Street and Old Broad Street.
The client's brief was to retain a 250 m facade along the front of 12 buildings, while reconfiguring the interior for office, retail and leisure space.
The troubled project began on site in summer 2000, but it was not until October 2001 that funding for the scheme was assured, when German bank Depfa provided a £130m loan. Construction was then hit by delays caused by technical difficulties, the weak demand for office space in the capital and problems arranging funding. Demolition work alone took a year because of the site's congested location.
Roughly half of the lettable area in the development has now been taken, boosted by the presence of jeweller Mappin & Webb.