NSW recorded 27 new local COVID-19 cases in the 24 hours to 8pm on Tuesday as Premier Gladys Berejiklian announced a widely anticipated extension of the lockdown for Greater Sydney – until at least July 16.

Just 13 of the new cases were in isolation for the entirety of their infectious period.

School students who were due to return from holidays next week will mostly learn from home, but schools will be open for children of essential workers.

Berejiklian warned case numbers would spike in the coming days due to the highly infectious Delta strain of the virus spreading rapidly in in the local government areas of Fairfield, Liverpool and Canterbury-Bankstown.

She warned that if the situation further deteriorated in those communities, harsher localised restrictions could come into force.

While current restrictions permit exercising in groups of 10 and care visits, the premier implored people in those council areas to avoid such activities.

“Most of us have stocked up on groceries, probably have more things than we need, so please avoid leaving the house, avoid going to indoor areas, avoid any activity unless absolutely necessary,” Berejiklian said on Wednesday.

In a bid to alleviate the financial hardship caused by the lockdown, the NSW government approached the federal government to reinstate the JobKeeper wage subsidy scheme – but were knocked back.

Berejiklian and Chief Health Officer Kerry Chant said there were instances of people in those council areas working or providing family support while ill. Ongoing wage support may have prevented such behaviour.

While the number of COVID-19 cases in the community remains stubbornly high, authorities said they had no choice but to prolong lockdown.

“This Delta strain is a game-changer – it is extremely transmissible and more contagious than any other form of the virus we’ve seen,” Berejiklian said.

“We don’t want to be in a situation where we are constantly having to move between lockdown, no lockdown, lockdown, no lockdown.”

Federal Treasurer Josh Frydenberg said some NSW residents were eligible for the Commonwealth COVID-19 disaster payment and the government wasn’t considering any other financial support at this stage.

Workers can get payments of $325 or $500, depending on the number of hours of work per week they have lost because of the lockdown.

Meanwhile, a fourth worker at SummitCare in Baulkham Hills has COVID-19, taking the outbreak at the facility to 10 people, including six residents.

However, the worker has been in isolation since Thursday.

More than a dozen other health alerts were issued on Tuesday night for venues mostly in Sydney’s west, as well as public transport routes.

Health Minister Brad Hazzard, meanwhile, said the lockdown may not have been necessary if vaccine supply issues didn’t exist.

“We’re doing our best to try and get as much vaccine as possible, get it into arms as quickly as possible and until we do, we face these risks,” he said.

Seven COVID-19 patients are currently in intensive care, including one in their 30s.