The Church of England began in the 1500’s. It is part of the Anglican Communion, which includes the Episcopal Church in the US, and a number of other related, but independent, churches in English speaking nations. Unlike the Eastern Orthodox, they do not have valid Holy Orders (in the view of the Catholic Church). C.S. Lewis 1898 - 1963 was an extremely important writer in the Church of England, and had a big impact on many Christians, including Catholics. The Archbishop of Canterbury is the head of the Church of England (along with the monarch, I think) and first among equals in the Anglican Communion (the 20 or so sister churches in other countries).
Historically there were 3 movements in Anglicanism: 1.) the High Church, more traditional and sacramental, Anglo-Catholic; 2) Low Church, somewhat similar to evangelical churches; and 3) Broad Church, which deemphasizes doctrine, more towards liberal, social action, politics. In the last 50 years or so, the Broad Church has grown stronger in the Church of England itself, and much stronger in Anglican sister churches in the U. S. and Canada. The Church of England has shrunk a great deal in recent years both in terms of church attendance, and influence on English society, though it still is technically an established church there. People in other countries sometimes refer to themselves as “Anglicans”, especially when they break off from the liberal Episcopal Church, but the Church of England per se would be only in England now. The Vatican has created an “Ordinariate” in England that attracts some Anglicans who want to convert to Catholic, but retain their Anglican culture and spirituality - which is a tremendous heritage.