The poll was run by Comres for the BBC, so I don't think 'poll rig' is a fair comment, although the questions asked are always relevant to the response. In this case the question is, I think:

The Queen is the Supreme Governor of the Church of England and is described as the Defender of the Faith, a title which goes back to the time of Henry VIII (the 8th). Prince Charles has suggested that if he becomes King, the title should be changed to Defender of Faith, implying he would see the role relating to all religious faith groups. Do you agree or disagree with each of the following statements about this?

The statements are:

The Queen and future Monarchs should keep the titles of Supreme Governor of the Church of England and Defender of the Faith. (73% agree)

The Queen and future Monarchs should not have any faith role or title at all. (25% agree)

If Prince Charles becomes King, his title should become Defender of Faith as he has suggested. (50% agree)

The Queen still has an important faith role. (79% agree)

Note the inconsistency between the answers to statement 1 and statement 3, suggesting a fair amount of confusion. There looks to be a fair proportion who are simply agreeing with the statements, without understanding them.

Not unsurprising results, given the level of sympathy still afforded religion in the UK, culturally if not in practice. In fact, I would say that the 25% agreement with statement 2 is encouraging (if respondents understood what was being asked - see above!).