Hackers target emails of UK's Gordon Brown: Report
Hundreds of other people may have also had their emails intercepted, perhaps as many as were caught up in the phone hacking scandal at News International's now defunct News of the World tabloid, the paper said.
Detectives were looking at evidence from about 20 computers seized from private investigators, the newspaper reported.
The team at London's Scotland Yard police headquarters were looking into the possibility that several newspaper titles commissioned private detectives to access computers, The Independent said, citing an unnamed source.
The Brown emails under scrutiny dated from the time he was Britain's finance minister before he became prime minister in 2007. Former Labour advisor and lobbyist Derek Draper was also targeted, The Independent said.
The Metropolitan police would not comment on the report.
"We are not prepared to give a running commentary on this investigation," a spokesman said.
News International, the British newspaper arm of Rupert Murdoch's News Corporation, also declined to comment.
The group closed the News of the World in July 2011 after evidence emerged that investigators working for the title hacked into the mobile phone voice mails of celebrities, politicians and even murder victims.
It is the only newspaper that has admitted phone hacking, although some journalists and celebrities have said the practice was widespread in the tabloid press.
News International's titles were not singled out in the Independent's report on email hacking.