"I'm at Piha protesting at the Government's reckless promotion of deepsea drilling risking Gulf of Mexico spill with Dads Army response capacity", Mr Twyford tweeted from the protest.
Ms Mackey has been a vocal critic of the Government's consent process under which Anadarko's drilling was approved and has questioned the ability of the company and the government to deal with a major spill in deep water.
Leader David Cunliffe last week also said the Government had not been honest with the public about the risks involved in deep water drilling.
Late last month he told the Herald Labour's position was that it would potentially support Anadarko's drilling if it met best-practice and environmental and clean-up standards, but it didn't yet.
Yesterday, however, Mr Parker said Labour did support Anadarko's drilling.
"It's legal and we're not saying we would close down existing consents."
"I'm not saying Anadarko's doing world's best practice because I simply don't know. What I'm saying is we acknowledge that what they're doing is legally in compliance with the law but we're going to tighten the law to ensure that world's best practice is met and that all future consents will require to be at world's best practice if they are to get approval.
"The industry tells us they're confident they can meet that standard. We're not reversing current approvals or banning duly approved drilling into the future."
He denied his party's position had changed.
"Our position is that we've been saying that the existing consent processes for deep sea drilling in our view are opaque and lax and it's unclear that New Zealand's got the response capacity if something goes wrong."