I think the way Cheryl Cole talks is just fine and find her accent pretty.
I don't think people should be prejudiced against her due to her style of English.
My background: I've worked with foreign languages for years, speak Spanish in particular, and have come into contact with non-native English speakers with a wide variety of accents. I relish linguistic differences!
I also have a tendency to start picking up the different accents of whoever I happen to be in close contact with on a daily basis, whether it be Japanese, Mexican, French, German ... I tend to pray the Our Father and Hail Mary with an Irish accent from listening to a Rosary CD by Dana.