The competition was also blighted by a war of words between the chairmen of the Royal Fine Art Commission and English Heritage.
Developer Blackfriars Investments withdrew its Will Alsop-designed conversion of Victoria House, Bloomsbury Square, from the competition last Thursday.
It cited as the reason a statement issued by English Heritage chairman Sir Jocelyn Stevens, who came down in favour of a Foster and Partners-designed option next to Tower Bridge.
It claimed that this public intervention by a statutory consultee made its position untenable.
Blackfriars Investments' head of development Richard Perett said last week: "Our withdrawal was prompted entirely by the outburst by English Heritage over what was supposed to be a confidential matter.
"Sir Jocelyn Stevens' comments prejudiced our participation in the competition because both cases required further discussions with English Heritage."
But Blackfriars Investments resubmitted its scheme on Monday, with the support of Royal Fine Art Commission chairman Lord St John of Fawsley. It claimed it wanted to provide a "genuine choice" in the competition.
Lord Fawsley said on Tuesday: "I think that Blackfriars Investments has shown a great magnanimity in coming back into the competition. It is doing this in the public interest."
Referring to Sir Jocelyn's statement, he said: "The RFAC does not take sides, but we believe the competition should be open, fair and untrammelled by inaccurate rhetoric from whatever source.
"Thanks to the letting-off of an ill-judged and unsubstantiated blunderbuss, the competition was blown out of the water."
Lord Fawsley continued: "The result is not important. What is important is to have a fair and open competition judged on the merits of the building designs, without the intervention of bombastic rhetoric from outside."
Sir Jocelyn responded in the London Evening Standard on Tuesday, saying: "Lord St John is a very unhappy bunny complaining in his burrow." Meanwhile, a DETR survey issued last Thursday found that, of 1033 respondents, 60% favoured London Bridge City and 34% preferred Victoria House as the site for the GLA headquarters.
A DETR spokesperson said this week: "We will continue to assess the two proposals against five criteria – the technical aspects, the environmental processes, cost, design and accessibility."
Both design teams are understood to be working up final schemes, which will be presented to the design panel and minister for London Nick Raynsford before he makes a decision in February.