The Tories' handling of allegations of Islamophobia has been "woefully inept" and they must now hold an independent inquiry, a former party chair has said.
Baroness Warsi said her party should learn from Labour's response to anti-Semitism allegations and not seek to use promises of action as a "fig leaf" to hide the true extent of the problem.
"Nothing tangible" had happened since she first raised the issue, she said.
The party said it took claims of anti-Muslim prejudice extremely seriously.
The Muslim Council of Britain recently complained that its own request for an inquiry had been ignored and accused the party of "turning a blind eye" to the issue.
It has compiled a dossier listing Conservative councillors and candidates who have been suspended or expelled following allegations of anti-Muslim prejudice.
It has voiced concern about the tone of Richmond Park MP Zac Goldsmith's 2016 campaign for the London mayoralty, and about social media messages shared by Harrow East MP Bob Blackman - who has strongly denied any allegation of anti-Muslim prejudice.
In an article for the Guardian, Baroness Warsi - who was the UK's first female Muslim cabinet minister - said both Mr Goldsmith and Mr Blackman should receive "mandatory enrolment" on diversity training courses.
The Conservatives' promise of voluntary courses for those who wanted them was "not enough", she said, warning the party needed to be "proactive and change its culture".
The peer said she had written to Theresa May about the issue and submitted a dossier of evidence but "absolutely nothing tangible" had happened in response.
The time for an internal investigation had passed, she said, and only a "forensic, wide-ranging and transparent inquiry" would now suffice.
The Conservatives say any members found to have behaved inappropriately have been suspended and investigations launched.