GRO Birth Registration
Henry Hadley, March Qtr 1839, reg. district Stourbridge Union, vol 18 page 481 - mother's maiden name Orford
Note - your describing "Lucy Maria, 1856, John William 1857 et al" as "Henry's siblings" did initially confuse.
Can find a couple of Henry's children (Harry Edward, Agnes Louisa) with mother's maiden name Teague on the GRO - but not Lucy Maria, first born.
FindMyPast has the marriage (transcription only) of Jane Teague, age 17 and Henry Hadley, age 19, on 5 Nov 1855. at Worcester. The Henry Hadley registered Mar Qtr 1839, would have been about sixteen and a half in Nov 1855 (assuming birth was registered shortly after his birth).