and non C of E denominations and religions usually do as well, on the grounds that some religion inside the state is better than none.
Queen 'should remain Defender of the Faith' - BBC poll
In a poll by Comres to coincide with the Queen's Diamond Jubilee, 79% of respondents said the monarch's religious role remained relevant.
Meanwhile, 73% said she should continue as supreme governor of the Church of England and keep the Defender of the Faith title first given to Henry VIII.
...
Farooq Murad, the general secretary of the Muslim Council of Britain, said the Queen's role in the Commonwealth meant other faith communities felt at home with her leadership of the Church of England.
"The largest Muslim countries, Pakistan, Bangladesh, Malaysia, are part of the Commonwealth and (people) arrive here having heard of the British monarchy from their fathers and grandfathers to the extent that many of them fought for the British Empire - we feel strong Christian values are good for us, we are very much on the same grounds."
http://www.bbc.co.uk/news/uk-england-18056322
The poll:
http://comres.co.uk/polls/BBC_Defender_of_the_Faith_Poll_April12_data_tables_rerun.pdf
50% thought a switch to "Defender of Faith" (ie dropping the 'the') would be a good idea for Charles's coronation.
At the next level down, a majority now want the automatic seats in the House of Lords for C of E bishops to be abolished:
http://www.brin.ac.uk/news/2012/house-of-lords-reform/
But there's not much chance of that - Lords reform (mainly about electing most of them, rather than having a few hereditary ones and appointing most for life) was quashed by Conservative backbenchers who were against it, and Labour would have joined them, to cause trouble for the coalition (showing they're not that worried about increased democracy themselves):
http://www.bbc.co.uk/news/uk-politics-19149212 .