"With New Zealand, we have shared scientific programmes and stewardship roles in the region," she said in a statement.
"This patrol has deepened that co-operation and will ensure fishing and other commercial activities in the Ross Sea region are carried out in line with international conservation agreements."
The HMS Protector usually operates in the British Antarctic Territory, near the tip of South America.
Former Antarctic diplomat Stuart Prior said the British were the latest major power to express an interest in the Ross Sea.
"People are looking very, very seriously at the Antarctic and Southern Oceans. As you know, the Chinese are taking a considerable interest in that part of the continent.
"Any country ... wanting to be part of the global debate about resources and sustainable management has to be present in some way in the Southern polar regions."
Mr Prior said the international interest did not necessarily reflect a push for resources such as fisheries.
"It doesn't herald a rush for toothfish or krill or anything else. It simply recognises that if you want to understand the health of the oceans, the way climate is changing, then the Ross Sea region is actually a superb laboratory.
"It highlights for us the significance of what is south of New Zealand. And so we should welcome the presence of British or Chinese because it is simply adding strength and depth to just how important our area is on a global scale."
New Zealand is attempting to establish the world's largest marine reserve in the Ross Sea, but has so far been thwarted by other countries which are signatories to the Antarctic Treaty.
The HMS Protector will be at Lyttelton Harbour until next Wednesday, and is open to the public on Sunday.
HMS PROTECTOR
• 90m long, 18m beam, displaces 5000 tonnes
• Maximum speed 15 knots (28km/h)
• 88 crew
• Deployed 330 days a year
• State-of-the-art technology includes ability to position with pinpoint accuracy in 80 knot winds.
