Addressing the Church of England's General Synod today, Methodist President the Rev David Gamble said: "Methodists approach the Covenant with the Church of England in the spirituality of the Covenant prayer.
"So when we say to God 'let me have all things let me have nothing', we say it by extension to our partners in the Church of England as well.
"We are prepared to go out of existence not because we are declining or failing in mission, but for the sake of mission.
"In other words we are prepared to be changed and even to cease having a separate existence as a Church if that will serve the needs of the Kingdom."
Their Covenant relationship together was, he said, "for the Gospel" and not simply an "irrelevant extra".
Rev Gamble's address was the first to General Synod by a Methodist President since 1993. A spokesperson for the Methodist Church said the President's address was a reflection of his strong commitment to the Covenant, rather than an expression of intention to re-join the Church of England. She denied the Methodist Church would be "swallowed up" by the Church of England or lose its name.
If that were to happen, it would likely anger traditionalist Anglo-Catholics in the Church of England, who differ with Methodists over aspects of the Apostolic Faith and bishops.
The Covenant was signed by the two Churches in 2003 after decades of dialogue aimed at closer unity. That dialogue continues within the Joint Implementation Commission, which has the task of overseeing the implementation of Covenant and its stated aims of overcoming obstacles between the two Churches and deepening relations.
The JIC has begun a second phase of work and is due to bring a report before Synod and the Methodist Conference in July 2011. The JIC's report from the first phase of work is currently making its way around Methodist and Church of England churches for consideration.
The Archbishop of Canterbury, Dr Rowan Williams, who is to address the Methodist Conference in June, told Synod it was "too premature" to draw any conclusions on the Covenant and expressed his hope that the addresses from the Methodist President and Vice-President would "galvanise enthusiasm" for seeing its aims fulfilled.
Methodist Vice-President Dr Richard Vautrey recommended the Churches expand areas of collaboration. He suggested the pursuit of peace and justice in the Holy Land as another issue they could come together on, in addition to social justice and climate change.
He said: "We can and do work together on issues of social justice, on issues that we both know God calls on us to challenge our society and our world. There is more that we could and should be doing together."
The British Methodist Church has nearly 270,000 active members, while the Church of England has 1.7 million.