A senior minister accused of repeatedly using taxpayer-funded drivers for non-work purposes has bowed to increasing pressure and quit cabinet.

NSW Premier Chris Minns had defended Transport Minister Jo Haylen after a series of car-related scandals in which she tasked a driver to take her to a boozy winery lunch and drop her children off at weekend sport in Sydney.

But Haylen announced she would quit her cabinet post on Tuesday afternoon, while continuing to serve in her local electorate.

“I’ve made some mistakes, people aren’t perfect,” she said.

“I did not break the rules, but I acknowledge that’s not the only test here … I’ve let the public down and I’m very sorry for that.”

Earlier on Tuesday, Minns said the revelations were a “black mark” on the government and “poor judgment” by Haylen. But he said he wouldn’t sack her, opting instead for changing the regulations on government drivers.

“Based on the information I have at the moment, I expect that the rules must be changed, and more importantly, the behaviour must change,” he told Sydney radio 2GB on Tuesday.

“If there’s other information and it comes to light and it’s presented to me … I have to take that into consideration, and it would weigh very heavily on me.”

Minns said ministers often worked weekends and Haylen was dropping her children off en route.

“[The driver] drove her from Caves Beach to Sydney to go to work, and on the way to work, the child was dropped at sport,” he said.

“In other words, the trip wasn’t so the kids could go to the sport on the weekends, the trip was so that she’d get to work.”

On Monday, Minns also defended the decision to use a ministerial driver to ferry Haylen and  Labor frontbench colleague Rose Jackson from her holiday house south of Newcastle to lunch at a Hunter Valley winery on the Australia Day long weekend.

The private journey – allowed under current ministerial rules – took the driver on a 13-hour, 446-kilometre round trip from Sydney.

Minns said he expected both ministers to learn from the error of judgment, but they would retain their roles.

“I’m not going to sack the ministers,” he said on Monday as he faced a barrage of questions.

“Both of them are in big portfolios … we need continuity in those jobs.”

Haylen had been battling a long-running industrial dispute with railway workers that has repeatedly threatened to shut down the state’s train network. Jackson, as mental health minister, is dealing with a staffing crisis as public psychiatrists resign en masse.

Haylen promised to pay back the $750 cost of the trip and acknowledged it did not pass the “pub test”.

She has previously come under fire for hiring former Labor staffer Josh Murray to lead the transport department and the apparent use of a public servant in her office for political work.