Wary of the dawn start, the others had driven on ahead and were all staying overnight at a hotel in St Bees.
In this sentence, "dawn start" means starting something very early in the morning—at or around dawn (sunrise).
So the sentence:
"Wary of the dawn start, the others had driven on ahead and were all staying overnight at a hotel in St Bees."
means that the others, knowing they'd have to get up very early the next morning (perhaps for a hike, journey, or event), decided to drive ahead of time and stay overnight closer to the starting point—in St Bees—so they could be ready and well-rested.
"Wary" here means cautious or not looking forward to the early wake-up time.
