Almost one in every 35 men could pose a sexual risk to children, new figures suggest.
The research by the National Crime Agency found that as many as 3% of men could be a potential sex abuser or have an interest in online child porn.
The NCA's deputy director Phil Gormley told the Mail on Sunday that of those, as many as 250,000 men were "true paedophiles" - attracted to pre-pubescent girls under 12.
He said a new approach was needed to protect children from potential abusers, saying: "If all we have is arrest and incarceration, that will not help them come forward.
"Like most people I am shocked by the estimated number who have this interest. It tells us some unhealthy things about human nature."
The issue of child sex abuse has been thrust violently into the spotlight in recent months and years through high profile scandals including DJ Jimmy Savile's sex abuse on an epic scale and the grooming gang scandals in Rotherham and Oxford.
Last week a new report by the NSPCC found that the number of children at risk of all forms of abuse in the UK had increased by 80% since 2002.
The NCA figures, based on academic and other sources, suggested that between one and three per cent of men had paedophile tendencies, with Mr Gormley telling the Mail: " Whatever the exact figure, it is big."
Writing in the same paper Karen Bradley, who was appointed the first minister for preventing abuse and exploitation last year, said society was at a "watershed moment" and needed to look at the reality of what was going on.
The Staffordshire MP, who is the mother of two sons, wrote: "Victims and survivors of abuse are, more than ever before, feeling confident to report their experiences. This is encouraging, but also an immense challenge.
"Because coming forward is never the end of it for a victim; because the damage of those experiences is so hard to undo; and because it is clear that far too many children are being damaged in the first place.
"But the Government can't solve everything and, more importantly, I don't believe that it should. We must all look unblinkingly at the reality. Raise our voices when we suspect a child is at risk and work together to find solutions. It will not be easy. But it can and must be done if we are to protect our children."
In November a self-confessed paedophile outed himself in a television documentary to ask for more help for people sexually attracted to children in a bid to stop them becoming criminals.
Channel 4's The Paedophile Next Door featured 39-year-old Eddie admitting openly on camera that he has been sexually attracted to girls as young as four since he was in his 20s, but insisting he had never committed a crime.
The programme suggests radical changes are needed to child protection that include treatment and therapy for those who come forward despite never having committed any sex offence.