Speaking at Westminster Cathedral, the Archbishop of Westminster Vincent Nichols said: "Talk of sin is not always popular - unless we are talking about other people's sins.
"In recent weeks the serious sins committed within the Catholic community have been much talked about.
"For our part, we have been reflecting on them deeply, acknowledging our guilt and our need for forgiveness.
"This is the journey of Holy Week.
"Indeed, to appreciate the message of this great Christian feast we have to begin with our own sin and shame."
And at St Mary's Cathedral in Edinburgh, Cardinal Keith O'Brien, head of the Church in Scotland, also apologised to abuse victims.
"Crimes against children have indeed been committed and any Catholics who were aware of such crimes and did not act to report them brings shame on us all," he said.