Hindu is a religion. A Hindu marriage is presumably one in which the bride, groom or both are of the Hindu religion or else the marriage ceremony is performed in accordance with the customs of the Hindu religion, and sometimes the parents choose who they want their daughters/sons to marry.
"English" means of or relating to the country of England, or its people. An English marriage would most likely mean one that takes place in England or one which takes place between English people.
Since Hinduism is one of the religions practised in England by English people, it seems apparent that the same marriage may be both "Hindu" and "English". Therefore there cannot be any inherent differences between the two.