Island Bay residents air their views on the new cycleway in December.

Some Wellington City Councillors claim a controversial new $1.7 million cycleway through the city's southern suburbs has blown its budget by $2m.

The suggestion has been categorically denied by the council's chief executive Kevin Lavery, who says the final cost of the Island Bay Cycleway remains on track to fall between $1.5m and $1.7m once it is finished in early February.

But city councillors Paul Eagle, Nicola Young and Simon Woolf all say they attended a meeting with Lavery and the council's chief asset officer Anthony Wilson on Tuesday, where they were told the cost had ballooned to $3.7m.

MAARTEN HOLL/FAIRFAX NZ Wellington City councillor Paul Eagle says the hotly-debated Island Bay Cycleway has gone $2m over budget, but council staff have rejected his claims.

Eagle – a long-time opponent of the cycleway's controversial design – said the trio were stunned when they heard the budget had more than doubled.

"Bottom line, heads need to roll. Ratepayers need to know that someone will be accountable for this reckless overspend."

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ROBERT KITCHIN/FAIRFAX NZ Reporter Amy Jackman road-tests the Island Bay cycleway, shortly after it was opened.

Woolf backed Eagle's account of the meeting, and said he was not surprised the project cost had blown out given its poorly-run public consultation, which sucked up a lot of time for a lot of "well-paid" council staff.

"This council is not good at putting a dollar figure on people's time," he said.

"I think there should be some accountability over this [project cost] because councillors did not sign off on that."

ROBERT KITCHIN/FAIRFAX NZ Many people are upset at the impact that Island Bay Cycleway has had on The Parade.

Young could not be contacted on Sunday, but in a Facebook post on Saturday she also quoted the $2m figure and said it was "outrageous".

Lavery did not return phone calls on Sunday. But council spokesman Richard MacLean said he had spoken with him, and he categorically denied any suggestions the cycleway had blown its budget by such a margin.

Lavery did not know what prompted Eagle, Young and Woolf to get that impression, MacLean said.

It was also not yet clear how much of the final cost would be born by Wellington ratepayers, as the council was still in funding negotiations with the New Zealand Transport Agency, he said.

The cycleway along The Parade in Island Bay has been controversial since it was first mooted in 2011, sparking protest groups but also attracting plenty of admirers.

The anger is largely over the fact it sits between the footpath and off-street parking, which cuts down the space available to vehicles and gives the unusual appearance of cars sitting 1.5 metres out from the kerb.

Its construction was delayed repeatedly until the builders finally moved in during September.

It was initially expected to cost $1.3m but that projection jumped to $1.9m before council officers returned to the drawing board in 2014 and produced a new design that sacrificed less car parking and removed a set of traffic lights at Dee St, which brought the cost down to $1.7m

Eagle said he would be seeking a full breakdown of costs for the cycleway, and an explanation as to why it has gone "even one dollar" over budget.

Woolf said the cost overrun would make it difficult for the council to convince the public that it was capable of delivering its proposed $101m programme of new cycle lanes across the city over the next 20 years.