The Pennington family tree, England

I have not managed to get very far with my family research, all i know is that my Grandmother was called Alice Pennington, and died in 1979(The year i was born), she never married but had a child called Barry Pennington in 1939?(my father). She lived as a child in a village called Pennington,in cumbria(lancashire area of England)and then later moved to Preston.If anyone has traced us and we are in your family tree please help me because i just don't know what to do next!