Officers said the figure was just the "tip of the iceberg" and added that more than 1,400 people including politicians, TV and music stars and religious figures were being looked into.
The National Police Chiefs Council (NPCC) said it had seen a huge rise in allegations since the Jim Savile scandal with reports increasing by 71 percent since 2012.
Schools, children's homes and sports clubs are all implicated.
Chief Constable Simon Bailey, the NPCC's lead for child abuse, said: "The referrals are increasing on an almost daily basis so the numbers I refer to today are a snap shot in time.
"There is no doubt in my mind that the Savile effect has played a significant part in giving victims the confidence to come forward and report abuse.
"The service now looks upon child abuse very differently and victims are getting and can now expect a very different response.
"But these figures do raise the question, is more abuse being perpetrated? I don't have the evidence at this moment in time to prove this one way or another.
"But I do know that the internet Is being abused in a manner for which it was never intended.
"And as a result I cannot help but think that more abuse is in fact being perpetrated. More research is going to be needed to prove this one way or another."
He added that there were no figures on the number of victims but that it was "fair to say that it is going to run into the thousands".