She wasn't jailed for drinking from the same cup fgs it's been on the BBC News website enough recently that you could at least get it right. Her Muslim neighbours and co-workers said the water they shared was unclean as she had drunk from it and she isn't a Muslim. There was a row and she apparently said things which to them were blasphemous. She was then questioned in front of a baying mob and admitted blasphemy and was jailed. The higher courts have heard her appeal and said she didn't get a fair trial and there's no evidence she committed the offence. Basically she admitted it in order to save her life.
I also think her family have listed a number of countries they have asked to give them asylum and I'm not sure the UK is one of them.