LONDON — The British police delivered a striking warning to crime victims on Monday: If you want the case to be pursued, be prepared to turn over personal data from your mobile phone, laptop, tablet or smart watches.

“Police have a duty to pursue all reasonable lines of enquiry,” Assistant Commissioner Nick Ephgrave, the National Police Chiefs’ Council lead for criminal justice, said in a statement. “Those now frequently extend into the devices of victims and witnesses as well as suspects — particularly in cases where suspects and victims know each other.”

But the new policy raised concerns about potential invasions of privacy and the risk of discouraging people from reporting crimes, particularly offenses like sexual assault that are already underreported because victims fear being treated like the guilty ones.

In many cases, the police already search digital trails, which can produce evidence that either backs up an accusation or casts doubt on it. Privacy advocates say that police departments often improperly download cellphone data from people they detain, without their knowledge or consent.