The two-track process which the Government decided to follow after receiving an unsolicited bid from a consortium from NZ Infra, a joint venture between the Super Fund and a Canadian pension fund, has come under fire.
This saw the private sector bid being compared against one being developed by the New Zealand Transport Agency.
Twyford defended the decision to have Cabinet choose between the two projects, because of the innovation it offered.
"We'd never seen anything like that, I think that was the right thing to do."
But the way the process has been handled has been slapped by transport groups.
Barney Irvine, the AA's Auckland Issues said Auckland light rail became a "quite bizarre procurement process" where a government plan was effectively bidding against a private sector bid.
As a result of the concerns, the AA formed a group with a diverse range of groups including the EMA, Heart of the City, Greater Auckland and Generation Zero to go to the minister with its concerns.
"The track we've been heading down just gave us no confidence at all in the sorts of benefits that were going to be delivered and was going to lead to a good outcome for the country," Irvine said.
The principal concern was that there was no visibility about what was being proposed or what it was being measured against.
"We had quite an extraordinary situation where just about everybody in the transport sector was really concerned about where it was heading," Irvine said.
"It had to go back to fundamentals. It just had to. There was just no alternative."
The AA hoped questions would be asked about the waste involved, as well as "some accountability around the decision making that led to the project being taken off the track it was on, only to be put on a completely new one that became a dead end".
Auckland mayor disappointed
Auckland mayor Phil Goff said the result was disappointing and frustrating.
"I am disappointed with that outcome, as I am sure many Aucklanders are too.
"It is frustrating that after three years, disagreement within the coalition has held this process up.
"It's now less than 90 days until the general election and we expect the incoming government to act quickly and decisively to outline its proposal to get light rail built.
"Tāmaki Makaurau needs a decision on light rail to meet growth on the Auckland isthmus, support intensification of housing, and head off bus congestion due to occur within three to four years - light rail needs to be in place before then."
National's transport spokesman Chris Bishop described the issue as an "epic fail" of a similar scale to Kiwibuild, saying it was one of Labour's first promises during the 2017 election.
"They said it would be built to Mount Roskill, not just started, but built from the Auckland CBD to Mount Roskill by 2021, which is just next year," Bishop said.
"After three years of work, millions of dollars to consultants and lawyers and policy advice, back and forth, we have no route, no consent, no business case, we have no plan, we have no estimate of the cost.
"Light rail's actually gone backwards compared to what it was three years ago."
Twyford maintained that the process would continue, with delivering it still Labour Party policy, but the private sector bid refused to say with certainty whether it would continue to pursue the contract.
"We are still digesting today's decision and, therefore, are not in a position to comment," a spokesman for NZ Infra said.
Ministers from NZ First have publicly questioned the need for the light rail project.
Earlier this month, NZ First leader Winston Peters indicated the issue was likely to be one considered as part of the election.
On Wednesday Peters denied blocking light rail "or any other rail" but that "as a fiscal proposition, with offshore proprietorship, it did not work".
The Canadian company which had partnered with the Super Fund described the news as a "significant disappointment".
"We gathered the best international light rail experts to put forward an integrated, inclusive and sustainable project that had the potential to spearhead the transformation of Auckland," CDPQ Infra managing director Jean-Marc Arbaud said.
"Our proposal was fully funded, deliverable and offered clear value for taxpayers. We diligently followed every step of the rules and process designed by the Ministry of Transport.
"It is disappointing that the process has been cancelled but we respect the decision of the New Zealand Government."
Matt Whineray chief executive of the NZ Super Fund said when the organisation entered the process it knew the outcome would be "uncertain".
Work on the light rail decision was part of the confidence and supply agreement between Labour and the Green Party.
Green MPs both welcomed the decision to end the current process, while also accusing NZ First of breaching the Government's agreements around the coalition.
Associate Transport Minister and Green Party transport spokeswoman Julie Anne Genter said she welcomed the decision to run the process through the public sector, rather than having Cabinet select the preferred option.
"With the twin track process over, detailed planning work on light rail can continue and key design and financing decisions can be taken quickly after the election," Genter said.
"Light rail will future-proof Auckland's transport network and ensure that the city can support a rapidly growing population. We have to get this right, so this is a good move at this time."
An advocates group for the trucking industry welcomed the decision, meanwhile.
"It's a gutsy move, but it's the right one, and I congratulate the Government on this decision. The estimated cost of $6 billion, if not more, for this project means the country cannot afford it," Road Transport Forum (RTF) chief executive Nick Leggett said.
"Unfortunately, Auckland Light Rail has proven hard to roll out and costs are always underestimated as the current City Rail Link debacle shows."