LONDON — The surprising defeat last month of a measure allowing the ordination of women as bishops has plunged the Church of England into a crisis with one issue at its core: Should religion adapt to fit an increasingly secular society, or be the enforcer of tradition in fast-changing times?

Debate over that question is upending Britain’s official church, the symbolic heart of a global Anglican Communion that includes the Episcopal Church in the United States. The narrow loss of the measure has so infuriated liberal church leaders that many insist the ­only way forward now is to show conservatives the door.