"continue undisturbed" is correct and usable in written English.
You can use it to describe a situation in which something is ongoing and uninterrupted. For example: "The children continued undisturbed in their playtime activities."
"At present," Mr. Buzek said, "it is my responsibility to ensure that all state functions continue undisturbed.
It's time the well-off in society stopped trying to sugar-coat Nigeria's harsh reality and expect the status quo to continue undisturbed.
According to the National Landlords Association (NLA), gangsters are attracted to rented properties for growing cannabis and manufacturing crystal meth because they are often in quiet residential areas where their activities can continue undisturbed.
Sally McDonald, chairman of the Brontë Society board of trustees, said: "These moors should continue undisturbed for generations to come and for the swathes of visitors from the UK and overseas drawn to Haworth and Yorkshire by their interest in the lives and works of the Brontës.
Peale sought to sabotage Longacre's attempts, with the goal of having him dismissed, and such work contracted for outside the government, allowing the medal business to continue undisturbed.
Arguing that a diminished capability for police to access such data was allowing organised crime to continue undisturbed, crimes to go unpunished and children to be abused, May said: "if we do not act we risk sleepwalking into a society in which crime cannot be investigated".
Events inside the palace continued undisturbed, much as they have been doing for a thousand years.
The US ambassador, Samantha Power, to the United Nations says talks about Iran's nuclear program are continuing undisturbed by Washington's decision to block Tehran's new ambassador to the world body.
Inside the palace, the ceremony continued undisturbed, and most of the ministers were not told of the shooting, which occurred about half a mile away, until after the ceremony.
In 1983, after Noriega had joined forces with the Medellin cocaine cartel, and Bush had become Vice-President and the coordinator of the Reagan drug war, Bush and Noriega met again, and Noriega's CIA contact continued undisturbed.
During the summer, this chorus of activity begins shortly after daybreak and continues, undisturbed, into the early evening, with some restrictions on Sunday mornings.
