Anglican Church officials in Nigeria deleted all references to Canterbury from their constitution, the newspaper reported.
The movie is the latest development in a running dispute within the Anglican Communion over homosexuality -- and the closest the church has come to a formal split, the Times reported.
Archbishop of Canterbury Rowan Williams -- widely regarded as a liberal -- has nevertheless consistently opposed liberalization of policy on homosexuality, the newspaper said. Communion with Canterbury has traditionally been regarded as a defining characteristic of Anglicanism.
The Nigerian decision comes weeks before conservative Anglican leaders from the Southern Hemisphere are scheduled to meet in Alexandria, Egypt, to take up issues of gay rights. The Times said some sources see the meeting as the beginning of a formal church schism -- with a new Anglican communion being founded to represent orthodox Anglicans.
The Nigerian Primate, Peter Akinola, has said in the past it is not necessary to go through Canterbury to get to Christ.