The London-based practice will not be working on the scheme's high-profile second phase, the new-build element, following the recent completion of phase one, the renovation of the existing building.
Contractor Bovis Lend Lease and developer Land Securities - in a private-public partnership with the BBC - have cited 'creative differences' as the reason for the split.
But the AJ has learnt that Richard MacCormac had become increasingly frustrated by a series of value-engineering exercises on his competition-winning designs.
The architect had a number of arguments with Bovis - to which he was novated - over losing elements of his scheme, including the huge subterranean newsroom and an innovative use of breakout spaces in the offices.
However, the most recent row was over plans for a vast glass wall, which was proposed as a visual link for the new and old elements of the scheme.
Artist Antoni Malinowski, who worked with MacCormac on the scheme, told the AJ that relations between client and architect were increasingly fraught in recent months.
'Richard was insisting on certain basic design elements that were at the core of the project - such as the blue glass wall - that the client was trying to undermine,' he said. 'They said they could not afford it.
'Richard was sticking to his guns. He was saying that there had already been many
other changes on the scheme.
'He told them that they should not change it otherwise there would be nothing of his scheme left,' Malinowski added.
And another source extremely close to MJP confirmed that the client-architect relationship had indeed gone sour.
'The split itself has come as a complete surprise,' the source told the AJ. 'There is
no way Richard would have wanted it to end like this.
'But it can be extremely upsetting when contractors insist on more cost-saving measures when there have already been a number of significant value-engineering exercises undertaken.'
These developments - which Eric Parry has described as 'a sorrow' - will further heavily undermine the BBC's credentials as a client, after it also made serious cost
savings on David Chipperfield's BBC Scotland building in Glasgow.
In 2002, the corporation's operations chief, John Smith, won a series of awards, including one from the AJ, for his work as a construction client.
The official statement from Bovis Lend Lease and Land Securities gives few formal reasons for the split.
'All parties wish to make it clear that [the split] is in no way a reflection of their opinion of the professional capabilities of MacCormac Jamieson Prichard, whom they continue to view with the highest regard,' it says.
It is understood that a new architect for phase two will be appointed imminently.