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."
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."
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BBC News - Child sex abuse is 'woven into British society' - Theresa May
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."
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."
more
BBC News - Child sex abuse is 'woven into British society' - Theresa May
