But he insisted that the two churches, which split in the 16th century, must still work towards the "distant" goal of unity.
He said they should join forces to deal with the challenges of an increasingly godless Britain and warned that Christianity must not be marginalised.
It comes after a Baptist nurse was suspended for offering to pray for an elderly patient, and The Daily Telegraph disclosed that all NHS staff face disciplinary action if they are found to have been "preaching" to colleagues or patients.
The Cardinal made the comments during his first appearance at the General Synod, the twice-yearly gathering of the governing body of the Church of England, which began on Monday afternoon.
He said: "Let me be frank. Your struggles with issues on Communion which deeply affect the unity of the Anglican Communion, affect us all. Divisions within any Church or Ecclesial Community impoverish the communion of the whole Church.
"We Roman Catholics cannot be indifferent to what is happening to our friends in the Anglican Communion and, in particular, in the Church of England.
"All I can say – and I would not want to be misinterpreted - is that it is only in a fuller and deeper unity that the truth and the demands of the Gospel are to be discerned. In this sense, unity is a prerequisite to truth and you should not settle for less – even if it takes time.
"So where does all this lead? First of all, I must say that we cannot give up on that ultimate goal even if it still seems so distant. It has to be visible and sacramental communion."
The Cardinal, who is set to retire as Archbishop of Westminster this year, went on: "Rather than focussing primarily on doctrinal convergence, important as that is, spiritual ecumenism promotes a living dialogue that gives room for an exchange of spiritual gifts that enrich us mutually as we get to know and appreciate each other’s treasures and so discover practices and ideas that can enhance our own Christian life and ministry.
"Our two churches, it seems to me, increasingly see that we have to face the challenges of our very secular society together.
"Christianity must not be marginalised in the public life of our country.
"And underlying all this is the fact that we now experience each other, as I myself have done, as friends, brothers and sisters in Christ, people attempting the same mission of bringing the Gospel to today’s world. I think this is hugely significant and a reason for great hope."
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(Source: DMUK)