An urgent search was launched by police, who found their bodies inside the overturned car, after it left the A4085 at Garreg, near Tremadog, and was partially submerged in water.
Rishi Sunak sent his sympathies to the boys’ families during Prime Minister’s Questions.
“I know the thoughts of the whole house will be with the family and friends of the four teenagers who died in a car accident in North Wales,” he said.
Crystal Owen, Harvey’s mother, wrote on Facebook: “I feel like I’m in a nightmare I wish I could wake up from but I’m not.
“I just wanted to say I do appreciate people’s kindness but no amount of messages is going to help me overcome this. Nothing will make this nightmare go away.”
She said she didn’t know the boys were going camping and thought they were going to stay at a friend’s grandfather’s house.
Superintendent Owain Llewellyn, from North Wales Police, said the crash appeared to be a “tragic accident” but that the investigation into why the car left the road is ongoing.
In an update on Wednesday, he said officers were now being assisted by members of the the North West Underwater Search Team and that the road would remain closed in the meantime.
In the Shropshire town of Shrewsbury, where the boys lived, the Trinity Churches parish said it would offer “time and space to pray” at the Trinity Centre in Meole Brace, from 9am on Wednesday.
Shrewsbury Abbey, meanwhile, is open all day for prayer, and Shrewsbury Colleges Group, where the boys were A-level students, offered “deepest condolences” to their family and friends.
Wilf’s girlfriend, Maddi Corfield, posted a tribute online for her “sweet angel”.
“I love you so much, I’m going to miss you forever,” she said.
“The sweetest and most loving boy I’ve ever known. I hope you know how much I love you, gorgeous.
“Thank you for all the time you’ve spent with me… thank you for loving me endlessly. I promise I’ll do the same for you, my sweet, sweet angel.”
She added: “I can’t imagine my world without you. I’m missing you so much already, but I am going to enjoy life the way you would’ve wanted, the way that you made me feel.”
Staff at the Dough and Oil restaurant in Shrewsbury paid tribute to Harvey, who worked with them.
The restaurant will remain closed on Wednesday as a mark of respect.
They said in an Instagram post he was “easy-going, warm, funny, gentle, bright, hardworking and humble”.
In a post of Instagram, they described him as “easy-going, warm, funny, gentle, bright, hardworking and humble”.
“He gave it his all, developing a passion for dough and had dreams of one day opening his own bakery,” they said.
“Our love, thoughts and condolences go out to Harvey’s family and to those of his friends, their lives full of promise cut so tragically short.”
Shrewsbury Town Council said its Christmas lights switch-on planned for Wednesday evening would not go ahead following the boys’ deaths.