After following all sorts of false trails I can finally come up with the following;
1891 Census,Rhyl Flintshire.
Jane Griffiths,Head widow born Ruthin Denbighshire c 1835.
John Griffiths Son born Ruthin Denbighshire c 1861.Grinder.
Mathew Griffiths Son born Rhyl Flintshire c 1867.Labourer.
Jane Griffiths Daughter born Rhyl Flintshire c 1871.
Amelia Anne Griffiths Grandaughter born Rhyl Flintshire c 1889.
RG12/4627/31/20.
1881 Census,Rhyl Flintshire.
Jane Griffiths,Head widow born Ruthin Denbighshire c 1833.
"Fay" Griffiths Son born Aberystwyth Cardiganshire c 1854.
John Griffiths Son born Ruthin Denbighshire c 1861.
Mathew Griffiths Son born Rhyl Flintshire c 1867.
Jane Griffiths Daughter born Rhyl Flintshire c 1871.
RG11/5528/19/3.
1871 Census,Rhyl Flintshire.
Jane Griffiths,Head widow born Ruthin Denbighshire c 1834.
Ann Griffiths Daughter born Tremadoc Caernarvonshire c 1851.
Theophilus Griffiths Son born Cwm Cardiganshire c 1853.
Emily Griffiths Daughter born Cerrig Y Drudion Denbighshire c 1856.
John Griffiths Son born Ruthin Denbighshire c 1861.
"Kayeswell" Griffiths Son born St Asaph Flintshire c 1863
Abraham Griffiths Son born Caernarvon Caernarvonshire c 1865.
Mathew Griffiths Son born Rhyl Flintshire c 1867.
Jane Griffiths Daughter born Rhyl Flintshire,8 months old.
Ann Jones Mother born Penmorfa Caernarvonshire c 1882.
RG10/5668/71/18.
All details are given as per Census entries as opposed to the Index on Ancestry.I'm afraid though as far as the Griffiths Family is concerned that is where the trail ends for I am unable to find any corresponding members of the Family in 1861.
Regards
William Russell Jones
Cefn Mawr
Wrexham.