It's entirely feasible, especially considering their ages. There have been cases where girls have gotten pregnant at eight years old- it's rare but it happens. The female body is capable of becoming pregnant anytime after she starts menstruating, and considering that the grandmother was in Romania, it is entirely possible that she was a Gypsy, which means she probably lacked access to birth control and sexual education.
As for the daughter, it's sad because she wasn't able to experience growing up, and now she's stuck with the burden of a child, which it will more than likely affect her schooling (if she's still enrolled), and her future because she has to take care of it. It doesn't make much sense, though, because England has a much better healthcare system, which would have allowed her access to birth control. But maybe not