http://www.bmibaby.com/bmibaby/terms..._check-in.aspx suggests an in-date passport is required to check-in online, while
http://www.bmibaby.com/bmibaby/terms...ification.aspx says they accept "all forms of identification" for domestic/ROI flights as long as it is "of a good standard". It may be that if you don't have a valid passport you are supposed to check in at the airport (which will cost you £11 plus credit card fee).