Chief of Defence Force Lieutenant-General Rhys Jones greeted Mr Hague before he laid a wreath at the base of stone frigate's anchor, which read: "In everlasting memory of those who died for our freedom."
He gave a respectful bow and stood in silence to pay his respects as the Last Post played.
The former leader of the Conservative Party then spent 20 minutes chatting with veterans of World War II, Korea, and Afghanistan.
Mr Taylor, 81, and serving president of the Canterbury Korea Veterans Association, was touched by the visit of one of the world's most powerful men.
"He has an appreciation of the past, and what New Zealanders have done in the wars over the years," the old soldier said.
"We had a lot to do with the British military in Korea and I've got a lot of respect for them.
"They've always liked Kiwis - we're a bit unconventional, we don't always follow their rule books."
While the emphasis has changed from last century's major wars to fighting against terrorism and rogue states, Mr Taylor says it's as important as ever for New Zealand to stand up.
Kiwi soldiers could teach other defence forces a lot in how they treated the local populations with respect and equality, said the former signalman and lieutenant, who lives in Woolston, Christchurch.
"We did it in Crete, Greece, Malaysia, Korea, and Vietnam, and I'm sure we've been doing it in Afghanistan and Solomon Islands too," he said.
Mr Hague said the UK was "very conscious" of the sacrifices made by the New Zealand Defence Force in Afghanistan, ahead of its planned pull out later this year.
He paid tribute to the 10 soldiers killed in the line of duty, including SAS corporal Doug Grant, who died after an attack by the Taleban at the British Council diplomatic offices in Kabul in 2011.
"These people have been doing outstanding work trying to bring peace and stability to Afghanistan and trying to help Afghans determine their own future without presenting a danger to the rest of the world," Mr Hague said.
"That reminds us of how closely we've worked together over a long, long period."
After meeting the veterans, Mr Hague was taken on a tour of the central business district's red zone by Earthquake Recovery Minister Gerry Brownlee.
British companies, especially those construction firms that worked on the "big scale" 2012 London Olympics, are interested in working on the city's $30 billion rebuild, he said.
Meetings were being held with local businesses today, he confirmed, as Britain looked to increase its trade across the Asia-Pacific region.
Mr Hague said New Zealand and Britain still enjoyed a strong economic relationship, even if it was "very different to the colonial days".
"There's a great history to our relationship but there is a great future as well," he said.
