Lawyers for Greenpeace are asking for the matter to be allocated an urgent hearing date due to the national importance of the issue.
Greenpeace chief policy adviser Nathan Argent said the judicial review would focus on Anadarko's current exploration of the Taranaki basin.
"But also, if successful, it could have an impact on any future drilling which could take place anywhere else."
Texas-based Anadarko plans to move the Noble Bob Douglas down to the Canterbury basin, off the Otago coast, to drill there early next year.
The legal challenge comes as Greenpeace plans to end its offshore protest today.
Mr Argent said all six boats in the flotilla would return to shore today, including the Vega, which has been within the Noble Bob Douglas's 500m exclusion zone for the last week.
Greenpeace executive director Bunny McDiarmid, who is returning aboard the Vega, said she would continue the campaign in the High Court.
"We've been here for over a week now, and we're heading home determined to carry on this campaign for a cleaner, more prosperous New Zealand.
"We're really happy to have had the support of thousands and thousands of Kiwis who don't want risky deep-sea drilling."
Green Party energy spokesman Gareth Hughes called on Anadarko to cease drilling until the legal issues around its permission to do so were decided.
He said the EPA had only seen summaries of Anadarko's oil spill modelling and emergency response plan.
Under transitional rules, the EPA had to consider the completeness of the environmental effects assessment, but not consider the actual environmental impact.
"That they couldn't even manage to do this is beyond belief. The process to give Anadarko the permission to drill has been an utter shambles and makes a mockery of the Government's claims of 'world class rules' protecting the New Zealand environment."
Anadarko this morning confirmed it had started deep sea exploration oil drilling off the Waikato coast.
The deep sea drilling of an oil well, more than 1500 metres deep, commenced at 2.30am by the oil exploration vessel Noble Bob Douglas, Anadarko New Zealand spokesman Alan Seay said.
"It's a process that's known in the industry as 'spudding' - it's the first step in the actual drilling protest - getting things set up on the sea floor and beginning the well."
It was estimated to take 70 days to drill down to Anadarko's target depth of 4600 metres, including a water depth of 1500 metres, Mr Seay said.
He said the Vega had not disrupted the drilling process.
"We've had to keep an extra eye out for them which we'd rather not have to do and whenever you've got somebody in close proximity in a safety zone, the safety risks are heightened, so we've had to take extra precautions to mitigate that."
Anadarko had not asked government authorities for any assistance to remove the protest vessels, however they had informed them of their presence, he said.
"We've notified the authorities, we did that last week, of the fact that the Vega's been inside that safety zone, but we're not seeking any particular intervention as such, that's always a call for them to make and so far they've seen fit to not actually go out there."
