Catholics could not be indifferent to divisions that "impoverished the communion of the whole Church", he told the Church of England's General Synod.
The Cardinal said there was a need for unity when both Churches were facing the challenge of a secular society.
Later this week the synod is to discuss the divisive issue of women bishops.
In his first-ever address to synod members, Cardinal Murphy-O'Connor said: "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.
'Greater unity'
"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."
The cardinal called for greater unity in the Church of England, adding: "Unity is a prerequisite to truth and you should not settle for less - even if it takes time."
On Wednesday, the synod will discuss draft legislation on allowing the consecration of women as bishops - which has divided the church.
It follows an agreement in principle last year to consecrate women bishops.
Some more traditional clergy and parishes oppose the policy and are demanding arrangements to allow them to function without compromising their principles.
But details of how the new arrangements will work have yet to be finalised.
The synod is also due to discuss the issues of human trafficking and whether clergy should be barred from joining the far-right British National Party.+++++++++++++++++++++++++++++++++++++++++++++++++++
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(Source: BBC)