The crackdown follows a furious backlash over the move to hand back killer Jake Davison’s shotgun and firearms licence weeks before the shootings. Davison, 22, went on a killing spree in the Plymouth suburb of Keyham last Thursday, killing five people.
The Home Office said forces will also be asked to revisit any existing gun licences.
The new guidance will cover social media checks of those applying for permission to own a firearm or shotgun.
A Home Office source said: “Incidents such as Thursday’s horrific events in Plymouth are thankfully rare, but their impact is profound, not only on those directly affected but on the public as a whole.
“We are bringing forward new guidance to improve how people applying for a firearms licence are assessed in future, including social media checks.
“But today, as a matter of urgency, we are asking the police to review their practices and whether any existing licences need to be looked at again.
“This will help to reassure people that all of the necessary checks have been made to keep them safe.”
Lord Stevens, the former Met Police Commissioner, had earlier urged police to check the social media accounts of gun licence applicants. He described Davison as “clearly a dangerous man” whose online videos were an insight into his character.
Lord Stevens said: “The videos he made should have been taken into account when he applied for a shotgun licence.”
Davison had used the internet to feed his obsession with guns before going on his murder rampage with a shotgun.
Witnesses have told how the crane operator had a “blank expression” on his face as he blasted his victims.
Davison shot dead his mother Maxine, 51, three-year-old Sophie Martyn and her father Lee, 43, Stephen Washington, 59, and Kate Shepherd, 66.
He also shot and wounded Michelle Parsonage, 53, and her son Ben, 33, who both survived.
The massacre ended when Davison turned the gun on himself.
For now, Devon and Cornwall Police will not discuss the return of Davison’s gun licence while an Independent Office for Police Conduct probe is ongoing.
The family of Mr Washington said in a statement yesterday: “Stephen was a friendly, outgoing person. He would help anyone at the drop of a hat. Stephen was a devoted family man, a loving husband, father, grandfather and best friend.”