The marriage is correct but if he doesn’t register you in a civil court, this means he is either married or intending to marry another woman which he can’t do in a civil marriage. He wouldn’t be able to get you a visa as you are not registered as his wife .

I have a Bangladeshi passport . One brother proposed marriage to my father for me and he is British, his father is from Egypt. He tells us that he don’t want to register the marriage in the civil court of uk but don’t mind to register it in the Islamic centre in uk . My father is just trying to safeguard my future. But he will never register it in the civil court .