Architectural watchdog CABE praised the practice's designs for the building last year.
The firm was one of three working on the scheme. Bob Delafield, executive at project developer London and Paris, said it had decided two architects were sufficient.
He said: "It is difficult to run with lots of different architects.
Co-ordination of design is needed at the detailed planning stage. Two architects were enough – Feilden Clegg Bradley was the unlucky one."
The practice had been working on a 7500 m2 civil courts building when it was taken off the project. Lifschutz Davidson is to take over its work. The third architect involved is London-based practice 20/20, which is working as masterplanner.
The move came after a decision to switch the court building from the corner of the site to another position next to St Peter's Square.
Feilden Clegg Bradley partner Richard Feilden said he was disappointed by the decision, but added that "not much of the work we have done on the previous location would be transferrable to the new location. It seems our design may be redundant. The whole process of procuring courts through private developers does have its difficulties".
Delafield said London and Paris had decided that the historic St Peter's Square would be a more appropriate setting than the the original location, which was at the junction of two city-centre roads. The developer is believed to be finalising a long lease with the council for the St Peter's Square site.
London and Paris was named preferred developer on the scheme last year and expects the court complex to be completed by 2005. The main building has eight courtrooms and six hearing rooms, and the overall scheme includes commercial and residential elements.
The client, the Lord Chancellor's Department, is expected to occupy the courts for 25 years.
A detailed planning application is expected to be submitted to the council in the next few months.