They have launched a new book entitled "Joint Statements" outlining areas of theological agreement between the two denominations.
The book was developed by the Catholic-Oriental Orthodox Regional Forum (COORF) and presented by the body's co-chairs Bishop Angaelos, General Bishop of the Coptic Orthodox Church in the UK, and the Catholic Archbishop of Southwark Kevin McDonald.
Bishop Angaelos said that the areas of common faith and witness outweighed the issues that had separated them for the last 1,600 years.
"It is very well for us to stand at our pulpits and preach love, but if our faithful do not see our Churches working together they see this as being quite hypocritical," he said.
"If we, as Church leaders, as priests and pastors and shepherds in the Church cannot actually portray this, if we cannot have this relationship and the wider relationship in this room and indeed between our Churches in this land that we live in, then we will find it very difficult to stand and preach love and forgiveness and acceptance, that is why I am very happy to be part of this launch."
Archbishop McDonald stated: "Even though in the past there were differences, they no longer justify the continued separation, and it is a call to the Churches to come together and move towards a closer communion.
"It is a good time for us to recognise that there is an international dimension to ecumenism and we all have a stake in it, we are all part of it."