How can one invite his English wife to Islam given the opposition from her irreligious parents?

Allah has permitted marriage to believing women and forbidden marriage to polytheistic women, with the exception of the People of the Book (Jewish and Christian women) if they are chaste. If your wife is a chaste woman from the People of the Book and not an atheist, there is no impediment to remaining with her, even if she refuses to embrace Islam. You should not despair of her guidance, and you have the right to keep her away from her parents if they are preventing her from embracing Islam.