Green’s Dictionary of Slang

accident n.

[euph.]

an illegitimate child.

[UK]J. Ware Passing Eng. of the Victorian Era 2/1: Accident. A child born out of wedlock.
[UK]D.L. Sayers Have his Carcase 322: Jenny Moggeridge’s Baby Charles what was a accident what Mrs Moggeridge was looking after.
Rebirthing N.Z. [Internet] Many children are unwanted, unplanned, ‘accidents’, or illegitimate.