Child sex abuse is "woven, covertly, into the fabric" of British society, Theresa May has warned.
Writing in the Daily Telegraph, the home secretary said the public were yet to grasp the full scale of the problem.
Her comments come after a new panel was announced for the parliamentary inquiry into historical child abuse.
Mrs May said the inquiry marked a "new beginning", but warned allegations made so far were only the "tip of the iceberg".
The inquiry was set up in July 2014 to find out whether public bodies had covered up or neglected allegations of abuse, following claims that a paedophile ring had operated in Westminster in the 1980s.
Mrs May said: "We already know the trail will lead into our schools and hospitals, our churches, our youth clubs and many other institutions that should have been places of safety but instead became the setting for the most appalling abuse.
"However, what the country doesn't yet appreciate is the true scale of that abuse."
'Tip of the iceberg'
She added: "During one of my first meetings with survivors, one lady said to me: 'Get this inquiry right and it will be like a stick of Blackpool rock. You will see abuse going through every level of society.'
"I fear she is right. I have said before and I shall say again, that what we have seen so far is only the tip of the iceberg."
Mrs May dissolved the original inquiry panel after two chairs were forced to stand down over their links to establishment figures from the 1970s and 80s, appointing a new chairwoman and re-examining the terms of reference.
Last week it was announced Professor Alexis Jay, Drusilla Sharpling, Ivor Frank and Professor Malcolm Evans would serve alongside Justice Lowell Goddard, a New Zealand judge, on the inquiry.
Prof Jay has expertise in social work and led the inquiry into child sexual exploitation in Rotherham.
Ms Sharpling is a qualified barrister with expertise in policing and the Crown Prosecution Service.
Mr Frank has experience in family and human rights law, and expertise in child protection matters.
Prof Evans is chairman of the United Nations subcommittee for the prevention of torture and professor of public international law at the University of Bristol. Educated in Cardiff, he has a Welsh perspective, which survivors have called for.
New terms of reference were agreed, including a removal of any cut-off date for claims.
The inquiry will have statutory powers to compel witnesses to appear to determine whether institutions took seriously their duty of care to protect children from sexual abuse in England and Wales.
Mrs May said she felt it was a "once-in-a-generation" chance to uncover institutional abuse, which she called "the darkness in our midst".