How to find more about my possibly Maltese great-grandparents?

My mum was taken into care when she was young, and she always thought that her mother was from Malta, although we managed to find out through Ancestry.co.uk that she was actually born in England. However, we cannot find any records of her parents anywhere - which leads us to believe that perhaps they were from Malta. Could anyone help us by telling us where we can possibly find more information, such as where they came from and when?