The scheme has been at the centre of a war of words between developer Land Securities and English Heritage (EH) ever since it was first unveiled last year.
However, the future of the building will now be decided by Communities Secretary Ruth Kelly, because the corporation had contravened its own tall building policies and had to refer the case to a public inquiry.
English Heritage has been very vocal ahead of the first round of debates, and has highlighted the building's design as one of the main reasons it is opposed to the scheme.
Paddy Pugh, head of advice for EH, even claimed that Renzo Piano's London Bridge tower would be 'easier to deal with', despite the tower being more than twice the size of the Walkie Talkie tower.
The fact, Pugh says, that the building does not taper at the top makes it a more 'oppressive' addition to the skyline.
Pugh said: 'This would become London's ugliest and most oppressive building. Londoners have not even been asked whether they want this building in their city.
'The harm it would cause to the historic environment outweighs any benefits the additional floorspace could bring to London's economy.'
Viñoly has been advised by developer Land Securities to remain tight-lipped about the inquiry. Land Securities has stated that any comment will come after the inquiry in two weeks time.
Meanwhile, Culture Secretary Tessa Jowell has announced that Britain's 24 World Heritage sites will be given buffer zones, preventing the development of skyscrapers nearby. The plans have been announced today, although it is not thought the announcement will affect the Viñoly public inquiry.
Public inquiry over Viñoly's 'Walkie Talkie' tower begins