Samuel's birth was registered in Chesterfield in Q3 1877 as Wragg with a mother's maiden name of Bowmer on the General Register Office index
WRAGG, SAMUEL BOWMER
GRO Reference: 1877 S Quarter in CHESTERFIELD Volume 07B Page 629
Here is a link to the same record on FreeBMD (which doesn't have maiden names before 1911) which you could add a source http://www.freebmd.org.uk/cgi/information.pl?cite=7f31fRClFARNh7IXP01QXw&scan=1
Unfortunately you have some mistakes in the profile. Samuel's mother wasn't Ann Bowmer. She didn't marry a John Wragg until 1880. His mother was Mary Ann Bowmer who married a John Wragg in 1873 in Chesterfield. It could be the same John Wragg (who perhaps married his deceased wife's sister?) or separate families. Mary Ann's mother's maiden name was Nightingale.
BOWMER, MARY ANN NIGHTINGALE
GRO Reference: 1854 M Quarter in DERBY Volume 07B Page 354
Here are all the other Wragg births with a mother's maiden name Bowmer.
WRAGG, JOSEPH NIGHTINGALE BOWMER
GRO Reference: 1874 S Quarter in CHESTERFIELD Volume 07B Page 632
WRAGG, FANNY JANE BOWMER
GRO Reference: 1875 D Quarter in CHESTERFIELD Volume 07B Page 623
WRAGG, MARY ANN BOWMER
GRO Reference: 1879 J Quarter in CHESTERFIELD Volume 07B Page 687
WRAGG, ANNIE LIZZIE BOWMER
GRO Reference: 1884 D Quarter in CHESTERFIELD Volume 07B Page 715
WRAGG, WALTER ERNEST BOWMER
GRO Reference: 1886 D Quarter in BAKEWELL Volume 07B Page 749
WRAGG, ANNIE BOWMER
GRO Reference: 1892 S Quarter in BELPER Volume 07B Page 619
WRAGG, WILLIAM ERNEST BOWMER
GRO Reference: 1894 D Quarter in BELPER Volume 07B Page 602
WRAGG, ALFRED BOWMER
GRO Reference: 1896 S Quarter in BELPER Volume 07B Page 623
WRAGG, SELINA BOWMER
GRO Reference: 1901 S Quarter in BELPER Volume 07B Page 673
WRAGG, WILFRED BOWMER
GRO Reference: 1904 M Quarter in BELPER Volume 07B Page 705
WRAGG, OLIVE BOWMER
GRO Reference: 1905 D Quarter in BELPER Volume 07B Page 616
WRAGG, BERNARD BOWMER
GRO Reference: 1910 D Quarter in BELPER Volume 07B Page 659