The Pope said the Catholic Church had not acted decisively or quickly enough to deal with priests who abused children.
Speaking to the press on board his plane, Benedict also said its top priority was helping victims heal and regaining their trust in the church.
The pope's comments marked his most thorough admission to date of church failures to deal with the sex abuse scandal, which has gathered pace with revelations in Belgium of hundreds of new victims, at least 13 of whom committed suicide over the years.
Benedict also said abusive priests must never have access to children, saying they suffered from an illness that mere "goodwill" could not cure.
The Pope acknowledged anti-Catholic protests planned for his visit, saying Britain had a "great history of anti-Catholicism. But it is also a country with a great history of tolerance".
He was also asked about Britain's history of anti-Catholic sentiment and polls that suggest the faithful had lost trust in the church as a result of the sex scandals.
He said he was shocked and saddened upon learning of the scope of the abuse, in part because priests take vows to be Christ's voice upon ordination.
He said he felt "sadness also that the church authority was not sufficiently vigilant and not sufficiently quick and decisive to take the necessary measures" to stop the abuse and prevent it from occurring again.
The pope said the victims were the church's top priority now.
He said he expected a warm welcome from Catholics and other believers and "mutual respect and tolerance" among those with anti-Catholic sentiments. "I go forward with much courage and joy," he said.