Find Ancestors

I'm trying to find any relatives I may have either in Ireland or the mainland UK. My mother's maiden name was Margaret Mary Byrne. She was born on (or around) 21st May 1933 and was brought up in a Dublin tenement. She lived in Frances Street and went to Francis Street school until 1940. Sometime (around 1941) in her childhood she lived in Drimnagh (not sure if it is spelt that way) about 3 miles away from Francis Street. I think she lived in Curlew Road. The school she attended was Morne Road School. She had 2 sisters and one brother all of whom were younger than her. Eldest sister was Nuala Claire (b. December 1936), her brother was Desmond Joseph (b Oct 1940) and her youngest sister was Sheila Anne (b. April 1944). Her father was called Matthew Byrne (b. December 1910) and he was a labourer in a factory. He had a brother, John Byrne, who married May and they had two sons, Tony and David. My mother's mother was Catherine Cowman (b. March 1909) Mum's best friends in Drimnagh were Jack Short, Patsy Salmon and Frankie Gallagher. Mum lost touch with her family when she was about 18 and has always wanted to trace them. If anyone out there can help I would be very grateful for any information. The O'Halloran's were in Oakham