Hey folks, thanks for the welcome!
My girlfriend is 5'10". She rented a Dawes (didn't check the model sadly) flat bar to go around the Isle of Wight last weekend and loved it, perhaps something along their lines.
Budget would be anything up to £300. We're just getting into it so don't want to splash out! I've seen some posts on the classifieds and bike such as the boardman posted today look ideal. I ride a cyclocross and love it.