Charlie Higson's The Enemy?
Charlie Higson's The Enemy is the first in a jaw-dropping zombie horror series for teens. Everyone over the age of fourteen has succumbed to a deadly zombie virus and now the kids must keep themselves alive.
When the sickness came, every parent, police officer, politician - every adult fell ill. The lucky ones died. The others are crazed, confused and hungry.
Only children under fourteen remain, and they're fighting to survive.
Now there are rumours of a safe place to hide. And so a gang of children begin their quest across London, where all through the city - down alleyways, in deserted houses, underground - the grown-ups lie in wait.
But can they make it there - alive?
Found with search terms of book adult zombies child survivors