Unvaccinated people in New South Wales could be barred from locations and denied movement freedoms even after the state achieves 80% double dose vaccination, with the premier, Gladys Berejiklian, warning vaccine-hesitant residents they will not be able to “let everybody else do the hard work and then turn up” for equal freedoms.

Berejiklian delivered the message when announcing 1,257 new cases and seven further deaths at a Covid update she held on Monday, despite insisting last week that the daily Covid press conference ritual would be abandoned from the beginning of this week.

Berejiklian denied she had had a change of heart, insisting she was “always scheduled to do today” to mark the milestone of new outdoor gathering freedoms that fully vaccinated residents received from Monday.

Late on Monday, health authorities announced that the local government area (LGA) of Yass Valley would re-enter lockdown for two weeks from Tuesday after a local Covid case was detected.

The measure is the first example of a regional LGA being plunged back into lockdown after those which had zero Covid cases for at least two weeks had their stay-at-home orders lifted from Saturday.

As the state continues its push to vaccinate its way out of lockdown, Berejiklian said she was worried by a “slight slowdown” in vaccination rates.

She and her deputy chief health officer, Dr Jeremy McAnulty, also shared concern over increasing case numbers in the City of Sydney local government area, with infection rates in suburbs including Redfern now dwarfing daily rates in some entire LGAs of concern that are under a tighter lockdown.

Regarding rules for unvaccinated people, Berejiklian said the state government has not yet finalised its plan for Covid restrictions once the 80% double dose milestone is reached.

However, she sought to distance herself from her deputy premier, John Barilaro, who earlier on Monday suggested that businesses who did not want to mandate vaccines for customers could wait “three to four weeks” after the 80% target was reached before his government would “then lift further restrictions including for the unvaccinated”.

Berejiklian would not commit to the government locking out unvaccinated people from certain settings even after 80% double dose coverage is achieved, but said if she chose not to, foreshadowed that she “might say it’s up to business to decide”.

She said private businesses could begin refusing entry to unvaccinated patrons to avoid risking becoming an exposure site and being forced to shut. She said this was businesses’ prerogative and not something her government could control.

“We’re still working on those plans. [But] I don’t want people to think they can sit back, let everybody else do the hard work and then turn up when it’s 80% and get everything else that vaccinated people are.

“That’s not the right message. I want to say it clearly that if you’re not vaccinated, you will not have the freedom or the freedoms that vaccinated people have even when we get to 80% double dose. And it won’t only be a government decision.

“I just want to send the very strong message that don’t assume you’ll get everything that vaccinated people get at 80%.”

Berejiklian was also asked about an ABC report alleging the NSW government waited two days to lock down all of Sydney after NSW Health realised authorities had not contained a birthday party outbreak at West Hoxton in June, however she did not directly address these questions.

Instead, she suggested that after receiving initial health advice about uncontained spread resulting from the party, she initially had faith in contact tracers because she “saw how they reacted and responded to the other strains we had”. “In fairness to them and to everybody involved, Delta is a game-changer.”

“I think people will judge us around Christmas time when they look back to see how things have transpired – the thousands of lives we saved and what freedoms we’ll experience then,” she said.

McAnulty was asked if contact tracers have become so overwhelmed that tracing has been largely left to business owners to conduct. He appeared to suggest contact tracing resources were being focussed to help businesses where authorities know workplace transmission is occurring, mostly in critical food and distribution and infrastructure businesses.

Berejiklian also said presiding officers of the state parliament’s lower house were currently considering whether to require MPs be vaccinated when parliament sits next month, and that she hopes they decide in favour of such a mandate. “I personally don’t want to go into a workplace or a venue where there’s unvaccinated people.”

On the day that broad vaccine eligibility was extended to children as young as 12, Berejiklian noted some parts of western Sydney now had first dose vaccination rates of up to 90%, but given the statewide first dose figure sits at about 78.5%, “that means there are pockets in our community which are well below the state average”.

There were 12 new cases in western NSW, with five in Bathurst, four in Dubbo, two in Burke, and one as part of an “outbreak” in Walgett. In the far west of the state, there were seven new cases, four of which were in Broken Hill, and the other three in the majority-Indigenous town of Wilcannia.

Of the seven deaths announced, three people were unvaccinated, while four were fully vaccinated but all had significant underlying health conditions.

There are now 1,189 Covid patients being treated inside hospitals in the state, and thousands more receiving hospital care in their homes to avoid exposure. There are 222 people in intensive care, with 94 on ventilators. There are two children aged under nine in ICU, four people aged 10-19, 13 people in their 20s and 23 people in their 30s.

Of Monday’s 1,257 new cases, transmission was highest in western and south-west Sydney. There were 239 cases in Canterbury-Bankstown, 133 in Cumberland, 131 in Blacktown, 128 in Liverpool, 64 in Fairfield, 59 in Penrith, 36 in Parramatta, 54 in Campbeltown, 26 in Bayside, 10 in Strathfield, 25 in Georges River, and four in Burwood.

Authorities are alarmed by Covid spread in the City of Sydney, and warned they are actively assessing whether to designate it an LGA of concern. There were 56 new cases in the City of Sydney, with 21 cases in Redfern alone, 10 in Waterloo and two in Glebe, understood to be mostly linked to shared high-density housing blocks. There were also 41 new cases in Randwick.