The culture secretary, Lisa Nandy, has said there is still a problem with exploitation and abuse in the media industry and a failure to properly deal with allegations after Russell Brand’s conviction for rape and sexual assault.

She said women who came forward were too often not protected by institutions across public life, including in politics, and that huge power imbalances meant speaking up came at a very heavy cost.

Nandy told the media industry that “time is up” to bring in systems to protect vulnerable whistleblowers, and said that while the BBC had taken action in recent years, other organisations still had to take the issue seriously.

Brand’s conviction on Thursday renewed scrutiny of how the UK’s entertainment industry has treated celebrities accused of abusing their power, with some women saying they feared that speaking out could harm their careers.

Brand faces sentencing on Monday after being found guilty of raping a woman and sexually assaulting three others.…