Mr Beveridge said in recent years the school had seen some of the harms from excessive smartphone use and wanted to take action.
"When we do see incidents of students being unkind or even bullying it is almost always invariably linked to some form of online activity", he said.
He added that phones had an impact on the mental health of pupils and were a "distraction from learning" even when kept in a bag or a pocket.
The school has bought mobile phone storage lockers so Year 7 students can safely store their phones during the day.
Mr Beveridge said when they introduced the scheme just before Christmas, 10 pupils handed in their phones.
Within a month more than half the year group had chosen to drop them off at the start of the day.
Among them is Mila, who said she "felt better" and "less stressed" without the worry of it going off in class.
Another pupil, Elliot, said his phone was a "really big distraction" and he had chosen to hand it in so he did not have to "think about it all day".
At the start of the next school year, the scheme will be compulsory for Year 7s and it may be rolled out to older year groups as well.
Mr Beveridge said headteachers across Solihull wanted to take "collective action" on the issue, which is why they had written a letter to parents.
It is not about being negative about technology, he added, but about making sure that everyone was aware of the risks.
"The hope is that sooner or later it will be the social norm not to buy a smartphone until young people are at least 14, maybe older.
"Then parents won't feel so much pressure," he said.
But at the moment parents, like Afifa Tufail, do feel a lot of pressure.
The mother has a son and daughter at Alderbrook School in Year 7 and Year 9.
They have "dumb" phones but she said she worried about them being "left out or standing out" for not having a smartphone.
She said the letter from Mr Beveridge had been "really reassuring".
On Tuesday night the school is hosting an information evening for 300 parents, where a panel of experts will explain the risks of overuse of smartphones.
Among those speaking will be Harriet, who is in Year 13 at Alderbrook Sixth Form.
She said she had had a phone since she was 11 years old, describing it as a "necessity".
But the 17-year-old said they were a "huge distraction" and said it was "crazy" that she had to use an app to lock her phone and all her apps when she was revising.
She said she had also experienced the "darker side" of the technology when last year a man had airdropped inappropriate photos to her at a bus stop.
"As girls you have to deal with that added pressure," she said.
The event had been partly organised by Claire Smith, the principal of nearby Tudor Grange Academy, which has been a phone-free school for many years.
The policy ensured students were safe, that they could socialise and play and that they were not distracted from learning, said Mrs Smith.
She added that she wanted to be involved in the event to open up the conversation beyond schools to families and the community.
She said parents felt peer pressure to buy smartphones for their children because it was becoming the norm for them to have one.
By sharing stories about some of the risks, she said she hoped it would help them make educated choices.