Speaking after an historic meeting between the two leaders at Lambeth Palace on Monday, Most Rev Justin Welby and Patriarch Kirill described the relationship between their two churches a "bridge of friendship" between their respective nations.
Bishop Angaelos, General Bishop of the Coptic Orthodox Church in the UK, told Premier's News Hour he joined Patriarch Kirill and Archbishop Justin at a liturgy service over the weekend, adding: "The speeches that I heard we about Christian unity, looking at human dignity and facing the struggles of the world at the moment.
"When we speak into public life and we say that we've met together and we see eye-to-eye on many of the important things that face us and face the world, than that of course takes away the demonisation that sometimes might happen.
"If we can, as Christian leaders, take away some of the tension and reintroduce some warmth into relationships and become reconcilers in tense situations, I think that is what we should be doing."
The Archbishop of Canterbury and Patriarch Kirill acknowledged current "tensions" between the British and Russian governments but the pair also affirmed personal commitments to achieving reconciliation.
Following the meeting, which was the first time an Archbishop of Canterbury and head of the Russian Orthodox Church have met in more than 50 years, Archbishop Justin's residence released a statement which said: "In faith, hope and love, founded on the Lord Jesus Christ, the Churches have been a bridge of friendship between the two countries for more than three centuries.
"The meeting today, and indeed the whole visit of Patriarch Kirill, is a historic event in the development of that relationship, which they pray will be nurtured and sustained through continued spiritual, cultural and personal interchange between their churches."
The occasion, which is the first time an Archbishop of Canterbury and a head of the Russian Orthodox Church have met in more than 50 years, comes as the British and Russian governments remain deeply divided over the conflict in Syria.
In a meeting with counterparts from nations including Germany, France and Italy on Sunday, foreign secretary Boris Johnson and US secretary of state John Kerry hinted at putting greater pressure on Russia over it's military support of Bashar al-Assad, saying they were moving towards bringing fresh sanctions against "the Syrian regime and their supporters".
Following an informal conversation between Archbishop Justin and Patriarch Kirill shared over lunch yesterday, a statement from Lambeth Palace also read: "It was acknowledged that tensions currently exist between the Governments of their two countries.
"Archbishop Justin and Patriarch Kirill agreed that the first loyalty of the Christian Church is to the Lord Jesus Christ, and they affirmed that reconciliation was the key ministry of the Church in situations of conflict."
Patriarch Kirill's trip to Britain commemorated 300 years of the Russian Orthodox Church in Britian but his schedule also included a meeting with the Queen and reconsecrating the Russian Orthodox Cathedral of the Dormition in central London.
Archbishop Justin was given an icon of the protective veil of the Blessed Mother of God from Patriarch Kirill, while Patriarch Kirill was presented with a specially bound album of the Treasures of Lambeth Palace Library.
Christian and foreign policy expert Philip Gardner says Patriarch Kirill's comments on Russian intervention in Syria and Crime illustrate how the Russian Orthodox Church affectively acts as a "public diplomacy" arm of the Russian state.
He told Premier Christian Radio: "I fear much of this trip has much more to do with white-washing than it does with discussing Christian unity and understanding between different churches."
"The established Russian Orthodox Church plays an essential role within Russia and outside of it, as a close ally of the Putin government, as a cultural legitimiser of the Russian government and it's policies."
Asked about the important of Kirill's presence in the UK to commemorate 300 years of the Russian Orthodox Church in Britain, Philip Gardner said: "It is a significant milestone.
"It is important that those of the Russian Orthodox faith in the UK feel welcome, valued and a part of our national faith communities."
Click here to listen to Philip Gardner speaking with Premier's Alex Williams:
Click here to listen to Bishop Angaelos speaking with Premier's Hannah Tooley: