Most people in England believe the Queen and future monarchs should retain the title of Defender of the Faith and Supreme Governor of the Church of England, a survey has shown.
Almost three quarters gave their backing to the continued link between the Church and state, while 79% agreed the Queen still had an important faith role.
But a quarter felt the Queen and future monarchs should not have any faith role or title at all.
The ComRes poll for BBC local radio also found opinion divided on a suggestion by the Prince of Wales that he might change the religious role of the monarchy.
Charles has called for greater understanding between people of different faiths and reportedly says he would rather see his role as Defender of Faith rather than Defender of the Faith.
Half of those surveyed agreed that if Prince Charles became king his title should be changed to Defender of Faith, compared with 35% who disagreed with the proposal.
The research also found some regional variations in attitudes to the faith role of the monarch.
Almost a third of Londoners (32%) agreed that the Queen and future monarchs should have no faith role or title at all compared with 19% in the South West.
The National Secular Society said the idea that the Church of England was of "any real significance" to the vast majority of people was not sustainable.
President Terry Sanderson said: "If the Queen declares an allegiance to, and indeed preferential status for, only one religion - as she did at her coronation - then it renders everyone who is not of that religion to be less than full citizens.
"Prince Charles's suggestion that he be 'Defender of Faith' would be a step forward, but the ultimate goal must surely be for the Church of England to be officially disestablished and for Britain to be a secular democracy that includes everyone of whatever creed or none, without privilege or disadvantage.
"No head of state, be they monarch or not, should express any religious preference, far less be under a formal obligation to sustain one."
In their coronation oaths, British monarchs promise to maintain the Church. They must also be full, confirmed members of the Church of England.
ComRes interviewed 2,591 adults in England between 30 March and 15 April.