Sydneysiders face tightened restrictions and abrupt border closures as authorities struggle to contain the city’s swiftly expanding cluster of COVID-19.

Late on Wednesday afternoon, the federal government declared the seven Sydney local government areas where the outbreak is centred a COVID hotspot.

Chief medical officer Paul Kelly said that would mean more federal government support to help fight the outbreak, including to keep it out of aged care and access to the federal stockpile of personal protective equipment.

Among the focus for state health authorities is a party in Sydney’s outer-south-west that has been labelled a “super-spreader event”. It is already linked to 10 infections.

Contact tracers are also desperately working to trace the origins of four mystery cases.

The so-called Bondi cluster had ballooned to 31 cases by Wednesday.

The list of exposure sites has also grown rapidly, with Joh Bailey hairdresser in Double Bay added on Wednesday along with two busy city restaurants.

• An updated list of exposure sites can be found here.

The index case in the outbreak is an unvaccinated Sydney airport limousine driver, who tested positive to the highly infectious Delta variant last week. Cases have spread rapidly since, with Bondi Junction’s busy Westfield shopping centre a prime focus for health authorities.

A swathe of virus restrictions were introduced across greater Sydney, the Central Coast, Blue Mountains, Wollongong and Shellharbour from 4pm Wedneday in efforts to contain the spread.

“Please abandon non-essential activities, please don’t attend social gatherings unless you absolutely must,” Premier Gladys Berejiklian said.

“I am not going to rule out further action.”

Health authorities announced 10 new cases of coronavirus on Wednesday, including seven previously reported on Tuesday.

There were also 13 additional infections that came in after the 8pm cut-off and will included in Thursday’s figures.

More than 44,000 tests were completed in NSW in the 24 hours to 8pm Tuesday.

Tweet from @NSWHealth

‘Super-spreader event’: CHO

Thousands of city dwellers have been told not to leave metropolitan Sydney as part of the raft of restrictions imposed on Wednesday.

Much concern centres around a birthday part in West Hoxton on Saturday. Among those who attended was a Bondi Junction worker who had the virus but was asymptomatic, and spread it to nine other people.

Eight of the 13 cases later cases announced on Wednesday were from the party, which NSW chief health officer Kerry Chant has described as a “super-spreader event”.

Dr Chant said there were people “unknowingly” infected in the NSW community.

A two-year-old girl who went to the party with her dad has also tested positive.

The toddler attended Little Zak’s childcare about 60 kilometres south-west of Sydney’s CBD on Monday.

Of the 30 partygoers, all have been told to isolate and get tested, while the daycare has been closed for deep cleaning.

Asked how the latest outbreak differed from Sydney’s Northern Beaches cluster late in 2020, Dr Chant said the the speed of transmission of the Delta variant was “particularly concerning”.

“We saw close contact but it would be the inadvertent contact you would have in retail settings that we would not have suspected transmission could happen as objectively,” she said.

Sydney restrictions tighten

Under NSW’s new rules, people who live or work in the City of Sydney, Waverley, Randwick, Canada Bay, Inner West, Bayside, and Woollahra local government areas cannot travel outside the metropolitan area unless it’s absolutely essential.

The metro area is defined as the Hawkesbury/Nepean River in the north/north-west and the outer boundaries of the City of Penrith, Camden Council, the City of Campbelltown and Sutherland Shire.

“We don’t want the virus to spread to the regions,” Ms Berejiklian said.

Household visitors are limited to five people, including children, and masks are compulsory in non-residential indoor settings – including workplaces – and at outdoor events.

Masks must also be worn to gym classes, which are limited to 20 people.

Borders close in all directions

The school holiday plans of thousands of Sydney families have been thrown into complete disarray as borders slam shut.

Just two days before public schools break for two weeks, Queensland followed Victoria and New Zealand by imposing bans on travellers from much of Sydney.

Tasmania and the Northern Territory have followed suit, while South Australia and Western Australia have also imposed travel bans.

• Related: Sydney COVID case travels to Wellington

Meanwhile, four NSW Nationals MPs who attended a Paddington pizzeria on Monday night are among those testing and isolating.

Agriculture Minister Adam Marshall, Ben Franklin, Trevor Khan and Steph Cooke dined together in Sydney’s east and later received a notification from NSW Health.

All four checked in with QR codes to the Christo’s Pizzeria eatery in Paddington.

-with agencies