His birth was original registered under her married name
So you have her previous married name. She married in 1938 but her maiden name was Brundle. Is that correct?
She had a child to that marriage - also in 1938
She had your father in 1945 and registered him under her married name but he was illegitimate
She married your grandfather in 1947
So we have quite a short time span for any other possible children prior to that 1947 marriage - 1939 - 1944 so I am puzzled as to why the list of births you originally posted went beyond 1947.
If she had other children between 1939-1944 - given she registered your father under her married name - wouldn't it be likely she would do the same with any others?
So you should be looking for births under her married name with maiden name Brundle between those dates