Wentworth Park  is the last remaining large green open space in the Pyrmont and Ultimo region, the most densely populated location in Australia, and is heavily used by residents and sports clubs.

It is set to come under further pressure as the nearby Sydney Fish Markets and Bays Precinct are redeveloped to include high-rise residential buildings.

Trees will be cut down and public access to the park will be reduced to accommodate the students for up to three years.

The Education Department has gained special planning approval to build the temporary school, according to project consultants McLachlan Lister.

Wentworth Park Sporting Complex Trust chief executive Peter Mann said the trust and the City of Sydney were supportive of the move, and the gross funding would come from the Education Department.

A City of Sydney spokeswoman said the school would be positioned to minimise its footprint on the park. "There are two small trees in poor health that may be removed and replaced with new trees," she added.

But as the  Education Department finalises a lease, a political battle over the long-term future of the Ultimo school amid an inner-city apartment boom is heating up.

The Greens education spokesman David Shoebridge is pushing for an upper house inquiry into the collapse of a deal between the City of Sydney and the Baird government for a larger school site that would have avoided the need to use Wentworth Park.

"This is clearly urgent," he said. "Key decisions are going to be made this year."

Greens MP for Balmain Jamie Parker said the decision to rebuild the school as a high-rise while putting students in demountables on a greyhound track was "appalling".

"It isn't the best solution for the education and wellbeing of the students," he said. "It's the cheap option."

Pyrmont Action's Elizabeth Elenius​ said families were moving because of the disruption to their children's education.

"They don't want their children in a temporary facility for three years," she said.

Ultimo P&C president Janine Barrett said she wanted the the Education Department to revisit the Fig and Wattle street site.

Urban Growth has revised its footprint for the Bays Precinct redevelopment to include Wentworth Park.

Mr Parker said it was a way for the Baird government to claim it was providing open recreational space for the high-rise residential buildings that have been planned for around the foreshore, but this ignored the fact the park was already heavily used.

According to its website, Urban Growth is considering proposals to close or relocate the congested Bridge Road, which separates the park from the waterfront, as a way to increase park usage.

An Urban Growth spokesman said the usage of the park would not be changed in 2016, and there would be consultation with stakeholders "prior to the implementation of any proposals".

A tender for the Sydney Fish Market redevelopment is expected to be announced soon.

Singapore company Oxley has announced its intention to bid for a commercial and residential redevelopment in partnership with Brookfield Multiplex.

It was an unsolicited bid by Brookfield Multiplex in 2014 to redevelop a swath of the waterfront and Wentworth Park that prompted the Baird government to call for "big ideas" for the entire Blackwattle Bay foreshore.