You were correct in that the form you state is that which can be followed by every denomination. It is particularly common in the Baptist and Free Church movements.
However, some churches have been known to insist on separate ceremonies.
Can I take this opportunity to apologise? Although my facts were correct, my tone was belittling and nasty. I didn't mean for it to sound like that; I guess that what with having to move and sort everything out, I've not been sleeping properly and I'm a bit strung out.
Sorry.
