A budget estimates hearing in the Legislative Assembly this week heard the trust's ACT branch had missed a deadline to commence a further appeal, but a related ACT Civil and Administrative Tribunal case was adjourned on Wednesday afternoon as lawyers confirmed papers had been filed with the court.

The case will hinge on the trust's legal standing to appeal the Heritage Council's decision to seek protection for about 40 per cent of the precinct, including the Dickson Towers, pair-houses, three-storey flats, maisonettes and garden flats.

Last month it lost an administrative appeal over the planned demolition, when ACAT ruled it had failed to respond to a public consultation within the designated four week period.

The National Trust wants the entire precinct given heritage protection, after a series of expert reports showed it was a unique example of post-war international modernist architectural style and critical to Canberra's history.

The trust's submission was made two days late after a public notice filed by the Heritage Council called for responses by October 22 last year. However, rules set out in the territory's Heritage Act required submissions to be received by October 20.

The council's error was caused by official processes related to public notification of the consultation.

On Wednesday, National Trust ACT branch spokesman Eric Martin said the organisation wanted to ensure the heritage debate was completed.

He said the development application for demolition of the dilapidated buildings was imposing on the heritage process, usually fully completed before redevelopment plans are made.

The interim listing was for the whole site, he said. "Their final decision was to list part of the site.

"The reasons behind reducing [protection] the site has never been made clear to us and we would argue there are some issues that weren't adequately considered in that decision making process, whatever it was."

Mr Martin called for adequate public debate about the decision to protect only the smaller sample of the 1960s site designed by Sydney Ancher for the National Capital Development Commission.

Chief Minister Andrew Barr has pledged to use every legal avenue available to push ahead with knocking down the buildings, which he has described as an eyesore on the entry to Canberra. The government wants to sell the land to fund the planned light rail line to Gungahlin.

Under Mr Barr's plans, just two of the Dickson Towers would be retained and a new small-scale museum created to recognise the precinct's history.

If the appeal is successful, it could see the heritage process start from the beginning. That outcome could see a delay of as much as six months.

Heritage Council chair David Flannery has previously said the government could call in decision making powers for the project.

Mr Martin rejected suggestions the buildings should be demolished because the community disliked their appearance on the busy road.

"Unfortunately they are not in the best condition because they haven't been well maintained. If they were in good condition, I firmly believe that the community perception would be quite different," he said.

The trust hopes legal costs for the appeal can be kept low through a quick resolution of the case.

Wednesday's ACAT challenge on the development application for demolition of the Dickson Towers, part of the wider precinct, was adjourned until late August as the Supreme Court case was imminent.