Todd was right. Henry VIII broke from the Catholic church because the Pope wouldn't let him get divorced from his wife so he could marry someone else. The ironic thing is that Edward VIII couldn't marry Wallis Simpson while he was King because the COE doesn't allow re-marriage after a divorce (this is why Charles is having a civil ceremony, not a church wedding, but it still doesn't make sense).
About 2 years ago the Church of England softened their stance on remarriage after a divorce - they now deem it ok (something again that was brought in to help Charles and Milla on their way to wedded bliss). However there is a slight sticking point - it's not ok if the person you are marrying is the cause of the first marriage failing. I think you can see where this leaves these two. Hence the civil ceremony.
So, Princess Margaret wanted to marry a bloke from The Who and Edward VIII wanted to marry some bloke called Wallis. Charles marrying Camilla seems pretty tame in comparison.