Yes presuming this Lady is Catholic, they dont allow Contraception, nor abortion, so that's in her favour. She needs to get the father to admit paternity, or somehow to prove he is the father, then if he is a British Citizen there is a strong possibility that she may be allowed to stay. Of course, none of this is easy at the best of times, and it's a darn sight harder to do when you are an overstayer/illegal. Good luck to your friend, Cherrysorra21.