“Dad, Dad — I’m going with these Order people.”
-- Dudley Dursley (DH3)
The war is intensifying:
“These accidents aren’t accidents—the crashes and explosions and derailments and whatever else has happened since we last watched the news. People are disappearing and dying and he’s behind it—Voldemort. I’ve told you this over and over again, he kills Muggles for fun. Even the fogs—they’re caused by dementors, and if you can’t remember what they are, ask your son!” (DH3)
Knowing that when Harry turns seventeen, Voldemort and the Death Eaters will be able to find him in Privet Drive, the Order of the Phoenix makes arrangements for Vernon, Petunia, and Dudley Dursley to go into hiding. Hestia Jones and Dedelus Diggle bring the Dursleys to a safe house for their protection as the sun is setting (“The car turned right at the end of Privet Drive, its windows burned scarlet for a moment in the now setting sun, and then it was gone”), just before Harry is to be transported away from Privet Drive for the last time. Uncle Vernon drives the car, which impresses Dedalus (“Very clever of you, sir, very clever. I personally would be utterly bamboozled by all those buttons and knobs”). The Dursley family drives off accompanied by Hestia Jones and Dedalus Diggle just before Harry is to be transported to the Burrow (DH3). They drive about ten miles from Privet Drive, then are taken by side-along Apparition to a place of safety.
The Dursleys leave just as the sun is setting on July 27, 1997, which would be just before 9 pm.