"A few months ago it became apparent to us that largely due to timing, we needed to make this application and it was a gathering of all of this information that we needed," Ms Squire said.
"It's so significant for Teina and for the New Zealand justice system quite frankly - it had to be done properly."
All three lawyers involved were offering their service pro bono, Ms Squire said.
"We were together when the documents were filed. We made a point of being together as a team and we'd spoken to Teina earlier and he knew that it was coming. He's always pleased to see some progress and humbled by the tremendous support that he's had from the public.
"He's aware of some of the documentaries and some of the fundraising efforts that are going on on his behalf and he's - I don't think it's too far to say - quite overwhelmed by all the support."
Pora's could be the last appeal from New Zealand to be heard at the Privy Council, Britain's highest court. His application has gone there because he started the appeal process before the establishment of the Supreme Court in 2004 - now the final court of appeal for New Zealanders.
Pora's lawyers remained hopeful he would be granted legal aid, but Ms Squire said that was down to the Attorney General, who would make a decision after the Privy Council had considered the appeal application.
Ms Squire said she had lent her services free-of-charge because she believed in the cause.
"I was aware of the case from Tim and Jonathan for some time and it's critically important for Teina's liberty and also for the New Zealand justice system."
Crown Law, which prosecuted Pora, had also been served with documents as part of the appeal process, Ms Squire said.
Pora was convicted of Ms Burdett's rape and murder in 1994 after confessing to police and found guilty again at a retrial in 2000. This was ordered after the semen in Burdett's body was found to belong to Malcolm Rewa.
Rewa was eventually convicted of Burdett's rape, but two juries couldn't decide about murder.
Pora's lawyers will argue his admissions cannot be relied on, citing new expert evidence on false confessions and criminal profiling.
Earlier this month Justice Minister Judith Collins admitted Pora may have been wrongly convicted.
Act leader John Banks, who was Police Minister at the time Pora was charged, the Police Association, Maori Party, Labour and NZ First leader Winston Peters have also questioned the conviction.