A key piece of Australia’s largest public transport project will open to passengers within months.

Full-service timetable testing has begun on the Sydney Metro City line, which provides the first underwater train crossing of the city’s famous harbour.

The metro train line runs from Chatswood in Sydney’s north, under the city centre and to Sydenham in the inner-west and is expected to be open to the public in August, the NSW government said on Monday.

About 1000 people will be involved in “simulated scenarios” as would-be customers while the last tests are run on the line.

The 15.5-kilometre twin metro railway tunnels are up to 40 metres below the surface and link to several new stations, including at the harbourside Barangaroo precinct.

The project, planned and commenced under the former Coalition government, has been hit with cost overruns since it was approved in early 2017.

The final bill for the Sydney Metro City and Southwest line is expected to be about $21.5 billion, up $9 billion on its initial price-tag.

The final stage of the project involves upgrading the heavy-rail line between Sydenham and Bankstown, in the city’s south-west, requiring a 12-month closure of the route.

It forms part of a wider rollout of metro services across the city, which combined constitute the nation’s biggest public-transport project.

A Sydney Metro West line will connect the city centre with Parramatta, while a third project will connect St Marys in western Sydney to the region’s new airport.

Premier Chris Minns said the metro lines were part of a “city-shaping” public transport project that would also support much-needed housing.

The state government has ordered the snap rezoning of areas surrounding dozens of existing and planned train and metro stations in a bid to add hundreds of thousands of new homes.

“If we are going to address the housing crisis, we have to build homes near public transport like this and that’s exactly what we’re doing,” Minns said.

– AAP