To simplify the search I have added findings in blue to your original list:
James HOPE b Apr 1805, m 25 Jun 1832 Mary FOGG (1818-1865), d Dec 1877
Children
Jane Ann (Anne) b 1832 d 1848 Mar qtr 1848 Ashbourne
John b 1835 d after 1861
Sarah Anne Hope b 1837, m 6 Jan 1859 Thomas HARWORTH d after 1861
Mary b Jun qtr 1838 Ashborne, d after 1861
Maria Fogg b Mar qtr 1840 Ashborne, m 15 Apr 1867 Joseph CARTER, d 1908
Elizabeth Ellen b Mar qtr 1842 Ashborne, m 12 Mar 1866 Frank Evans JONES
Thomas b 1844, (birth reg not found), m Dec qtr 1869 Agnes Ann LAWRENCE, 2 children, ?d Sep qtr 1910 Chorlton
Harriet Emily b Dec qtr 1845 Ashborne, m 24 Jun 1874 James WHITAKER
Lucy b Dec qtr 1847 Ashborne, bap 14 Nov 1847, d after 1851
Clara Esther b Dec qtr 1849 Ashborne, d after 1861
Emily Louisa Emma Louisa b Jun qtr 1852 Ashborne, d after 1861
George b Dec qtr 1853 Ashbourne, m Harriet, d 1895
James Henry b Dec qtr 1857 Ashbourne, m 11 Apr 1907 Eva Gertrude LOMAS
Births registered HOPE mmn FOGG
Mary - Jun qtr 1838 The Ashborne vol 19 p358
Maria - Mar qtr 1840 Ashborne vol 19 p339
Elizabeth Ellen - Mar qtr 1842 Ashborne vol 19 p365
Harriet Emily - Dec qtr 1845 Ashborne vol 19 p356
Lucy - Dec qtr 1847 Ashborne vol 19 p321
Clara Esther - Dec qtr 1849 Ashborne vol 19 p337
Emma Louisa - Jun qtr 1852 Ashborne vol 19 p439
George - Dec qtr 1853 Ashbourne vol 7b p409
James Henry - Dec qtr 1857 Ashbourne vol 7b p461