Thank you everybody. Yes, she was Margaret Birkett and gave birth to Removed Birkett in 1934. She got married in 1938 and returned to Bishops Castle with the baby and the new husband.
I haven't applied for the 1934 birth certificate yet, maybe I should.
Maybe it was just a private arrangement and we will never find out who the father was.
The gentlemen in question is still with us and says he hasn't got his birth certificate. It seems his birth wasn't register for nearly 12 months!