The force has insisted the two men last seen with Slater “don’t have any relevance” to the case and has allowed them to return to the UK.
But Slater’s father, Warren, 58, said he “can’t understand” why the men had travelled with his son to Masca, saying: “You just don’t disappear.”
Speaking to The Telegraph on Wednesday, he said: “My only question is, and this is where you start the investigation from, why did two grown men take a young boy to a valley to a bed and breakfast? I can’t understand that.
“Why? You need to ask them why and then start from there. Spanish police must know. It is frustrating. It’s a language barrier and you can’t get mad at Spanish police because they don’t like it.”
Slater Snr spoke to The Telegraph after spending two hours searching the natural park in north-west Tenerife where his son vanished. He was joined by his other son, Zak, 24, and Slater’s uncle, who did not want to be named.
Searching at the hottest point of the day, the trio followed a mountain path down the barren valley and looked inside two abandoned shacks, which sit just a few hundred metres from where Slater’s phone was last traced.
Slater Snr, dressed in a black T-shirt and blue shorts, cut his legs and arms as he looked for his son. He said he was doing a “Columbo bit”, referencing the US TV detective.
Pointing to a large mountain peak in the distance, he said: “If someone told me ‘he’s up that hill and you’ll find him’, I’d climb that f---ing hill and find him.”
He added: “If I had mountain boots and some ropes I would go for it, but I can’t do it in Adidas Sambas.
“All I’m doing is a Columbo bit myself. I mean, he might be on here, you never know. But as a dad, I don’t want him to be.
“You just don’t disappear. He’s a young boy. He’s fit. He’s fitter than us all put together. He’s played football all his life. He’s fit as a flea. You just don’t disappear.”
He added: “I’ve taken him on many a trail when he was a kid, up where we live. He doesn’t know this area, but when he was a kid, I took him up Pendle Hill.”
Slater’s family have stayed in Tenerife to search for him. His father and mother, Debbie Duncan, 55, visited a police station in Playa de las Americas for two hours on Tuesday to demand answers about the investigation.
Spanish police have so far dismissed any criminal element to Slater’s disappearance, but officers in forensic gear have been seen searching the cottage in Masca where the teenager stayed before he vanished.
Slater said he felt “in the dark” about the police investigation.
He said: “The police are just doing their own investigations. They’re not telling us anything. They’re not telling you lot (the press) anything. We’re in the dark.”
He added: “I’ve gone past the sadness bit and I’m angry, if that makes any sense? I’m angry that nothing’s happened.
“They (the police) know best. Do you think they should still be searching? If it was in England I’d be making a stink but we’re in a foreign country and we’ve just got to leave it to people who know best.”
Slater, who had travelled to Tenerife with two friends, left a music festival in a car with two British men, who are believed to be in their 30s or 40s from southeast England.
After setting off from their accommodation he rang a friend and said he was lost, thirsty, had 1% charge left on his phone and had cut his leg on a cactus. His mobile ran out of power shortly after the call.
Asked if he thought Slater may have been headed towards the sea, which is visible in the distance, his father said: “Maybe.
“It’s not that much of an area,” he added. “They’ve (the police) got the resources, surely they’ve scoured it. We followed the path all the way down the valley.”
Duncan said on Tuesday that “words cannot describe the pain and agony” her family is experiencing.
Speaking through the missing persons charity LBT Global, she said: “Jay is a normal guy who is in his third year of an apprenticeship, and he is a very popular young man with a large circle of friends.
“We are a very close family and are absolutely devastated about his disappearance. Words cannot describe the pain and agony we are experiencing.
“He is our beautiful boy with his whole life ahead of him and we just want to find him. We do not have any information on his whereabouts.”
Timeline of events:
- Sunday 16 June - Jay and friends attend the NRG music festival. Between 03:00 and 06:00 local time he got into a car with two men he had met during the holiday
- Monday 17 June - Jay posts a picture on his Snapchat at a property in Parque Rural de Teno. Between 8.30am and 9.00am Jay calls his friend and says he missed a bus and was going to walk the 11-hour journey back
- Monday 17 June - Phone’s last location showing a path in Rural de Teno park
- Monday 17 June - Unconfirmed reports of Jay watching Euro 2024 matches in Santiago del Teide
- Tuesday 18 June - Jay fails to return to his hotel in Tenerife. Police and rescue teams begin searching and his mother and brother board a flight
- Wednesday 19 June - Drones, dogs and a helicopter are used to search Rural de Teno park
