Six schools in the West Midlands, four in London and four in Cornwall received calls on Tuesday morning.
A group reportedly calling itself "Evacuators 2K16" appeared on Twitter to claim responsibility, but the BBC was unable to verify the claims.
The National Police Chiefs' Council said forces were treating the threats "extremely seriously".
"At this stage there is no information to suggest the incidents are terrorist-related, however inquiries continue to establish the facts," a spokesman said.
"Forces are working together to investigate who is responsible and whether incidents are linked."
West Midlands Police said the calls to six schools in its region posed "no credible threat".
Bristnall Hall Academy in Oldbury was one of six West Midlands schools targeted, but reopened for pupils at 11:00 GMT.
Principal Vince Green said it was "incredibly frustrating" for the school, having had to close for one day last week after a similar threat.
"Last week there was a lot of anxiety because people weren't clear and when we did it again today people were quick to work out that it was a similar incident," he said.
"We have to take the safety of our young people and our staff very very seriously."
In Cornwall, four schools in Penzance, St Ives and Truro received calls at about 08:00 GMT.
Devon and Cornwall Police attended an hour later and said nothing suspicious was found.
Jan Woodhouse, head teacher at St Ives School, emailed parents to say pupils were returning to classes as normal.
"The site has been thoroughly checked by the police and given the all clear," she said.
"Although we are a bit wet the rest of the day will run as usual."
The four London schools were evacuated as a precaution.
The Met was treating the calls as "malicious communications".
Thousands of pupils were evacuated as hoax bomb threats were made to 14 schools across England.