Campaigners called for the law after Sarah Payne's murder
A man has been arrested after a worried member of the public raised concerns using the new "Sarah's Law" phoneline.
The scheme, launched on Monday, allows parents in four areas to ask police if anyone with access to children has convictions for child sex offences.
Police in one area, Warwickshire, said four calls had been received and one prompted police to take "immediate action".
The campaign for a law began after the murder of eight-year-old Sarah Payne.
She was murdered in 2000 by convicted paedophile Roy Whiting.
Det Ch Insp Debbie Tedds, from Warwickshire Police, said: "One of the calls received was from a member of the public raising concern about a child and as a result immediate action was taken to protect children at risk.
"A man has been arrested and inquiries are ongoing. Agencies in Warwickshire were not previously aware of the child or the circumstances."
The other areas taking part in the trials are Peterborough, Cambridgeshire, Southampton and Stockton in Cleveland.
The year-long pilots were launched in response to demands from parents to know where convicted paedophiles were living.
'Lots of inquiries'
Since Monday, about 36 members of the public have made requests for information under the scheme, but not all were from within the pilot areas or fell within the scope of the scheme, police said.
Cleveland Police said the force had received 16 calls in four days, and the same number were received in Peterborough.
No applications which fell within the pilot were received in Southampton, Hampshire Police said.
A spokeswoman for the force said they had received "lots of inquiries from outside the pilot area".
"We would encourage anybody who has concerns about the safety of their children to come into a Southampton police station and give us details," she said.
Cambridgeshire Police said some of the calls had not been relevant because the people being asked about did not have regular, unsupervised access to children.