Cardinal Vincent Nichols said some adoption agencies acting in the name of the Catholic Church were "lacking in care and sensitivity".
The Archbishop of Westminster will appear on an ITV documentary, Britain's Adoption Scandal: Breaking The Silence, in which women speak about their traumatic experiences of having their babies adopted via the Catholic Church, the Church of England and the Salvation Army, among other organisations.
Lawyers for the woman are calling on Home Secretary Amber Rudd to launch a public inquiry into the scandal.
Following allegations made in the programme, the Cardinal said: "The Catholic Church understands and acknowledges the grief and pain caused by the giving up of a child through adoption.
"The practices of all adoption agencies reflected the social values at that time and were sometimes lacking in care and sensitivity. We apologise for the hurt caused by agencies acting in the name of the Catholic Church."
Carolynn Gallwey, from Bhatt Murphy Solicitors, is preparing a case for an inquiry into the issue.
She said: "These women were told not to speak about what had happened to them. But now they're entitled to have their experiences recognised and the only way to do that is through a public inquiry."
Peter Williams - a commentator from Catholic Voices - said that lessons have been learned from what he called a "harrowing" chapter in Church history.
He told Premier: "Hopefully the lessons learnt from this are that the way that you treat people who have sinned - and the way you deal with the consequences of that sin - have to be based not just in justice but, as Pope Francis would say, in mercy."
In 1976 a change in the law gave local authorities responsibility for handling adoptions in Britain.
But in the 30 years before half a million adoptions took place, mostly of babies born to young unmarried mothers. Most were overseen by voluntary organisations, the majority of which were religious and whose social workers were known as moral welfare officers.
