Is this your family?. These births would seem to serve your interest in locating this family during the 1870s?
GRO BDM birth
WATTS, Lizzie Florence mms CASTLE
1873 SepQ Kingsclere Vol 02C Page 210
WATTS, Harry mms CASTLE
1876 MarQ Wimborne Vol 05A Page 293
WATTS, Blanche mms CASTLE
1877 SepQ Wimborne Vol 05A Page 274
WATTS, Frank mms CASTLE
1878 DecQ Thirsk Vol 09D Page 433
WATTS, Ruth mms CASTLE
1881 MarQ Thirsk Vol 09D Page 413
WATTS, Alice mms CASTLE
1882 JunQ Thirsk Vol 09D Page 441