A survey shows four in ten clerics think the Church should be more independent.
Polling by YouGov for the Religion and Society Programme also found a large minority thought it would be a good idea to split the Anglican Communion based on controversial issues like gay marriage.
Results show the disagreement between the Government and Church on gay marriage had led to more support for separating the Church.
One in seven clerics want full disestablishment of the Church of England whilst three in 10 only want some ties kept, according to the survey.
It found that 54% wanted to keep the established status.
It also showed that around half of clergy think equality laws in Britain mean Christians are being discriminated against.