There is a Henry William Gillard whose birth was registered in Yeovil (Ashington was in the Yeovil district) in 1856. His mother's maiden name was Bishop.
A William Gillard married Eliza Bishop in Yeovil district in 1852, so they are probably his parents.
GILLARD, HENRY WILLIAM Mother's maiden surname: BISHOP GRO Reference: 1856 D Quarter in YEOVIL Volume 05C Page 514
FreeBMD Marriages Jun 1852
Gillard William Yeovil Vol 5c Page 895
Marriages Jun 1852 (>99%)
Bishop Eliza Yeovil Vol 5c Page 895
Henry Gillard married Sarah Ann Penny in Bradford on Avon in 1879:
FreeBMD Marriages Mar 1879
PENNY Sarah Ann Bradford upon Avon Vol 5a Page 155
Marriages Mar 1879
Gillard Henry Bradford,W. 5a 155