Divorce in practice was the same for the Church of England as it had been for Roman Catholics all through the Middle Ages- if you were well connected or had lots of money, you could get a divorce. It was not absolutely forbidden, as it was in the Catholic Church, but still the political and financial connections were necessary. Although divorce was frowned upon heavily and had been forbidden by the Catholics throughout the Middle Ages history was filled with divorces and annulments for political reasons, as it was with arranged marriages between first cousins which was supposedly forbidden also. Arranged marriages were arranged for political and financial reasons- royalty married royalty and nobility married nobility, unless the royalty or nobility needed money, in which case the marriage to the daughter or son of a very wealthy commoner could be arranged, with the commoner of course becoming ennobled.
This very issue is the reason why Elizabeth's father, Henry VIII, had split from the Catholic Church. He wanted a divorce from Katherine of Aragon. The Pope would have let him have a divorce, only her brother was Henry V Hapsburg, who was at the time King of Spain, several smaller countries and Holy Roman Emperor. Henry V threatened to sack Rome and hang the Pope if the divorce was granted, so Henry VIII opted for Protestantism, which left him the head of his own church.
It was allowed with a special bull issued by the pope or leaders of the Church of England. Some of the reasons included prior contract in marraige (and the other person they were contracted to marry was still alive at the time the marriage took place) or the wife was unable to have children. Wives were usually sent to a convent and the husbands remarried.
They could refuse to marry but since parents did not take into consideration their childrens desire to marry, it was inmaterial if they were happy with the arrangement or not. Children did want they were told to do and parents often arranged 3rd or 4th marriages for their children as needed.