Belinda,
On buying Death Cert from Alnwick Reg Office......
On 1861 census William/Mary Taylor are living in the community of East Ditchburn, within the Township of Ditchburn, within the Parish of Eglingham.
On 1871 census, widower William is still living in East Ditchburn, ditto, ditto.
So Mary died between the two censuses, very likely in the community of East Ditchburn.
The stone you have seen corroborates this and gives the death date as
29th August 1868, aged 38 yrs.
The GRO Death Registration Index, as reproduced onto FreeBMD web site, reveals that her death was registered in the Sept Qtr (i.e sometime between 1st July and 30 Sep) with/at Alnwick Reg District office. But however "informed" of her death, told Registrar that she was aged 37 !
1861 Census ( which was taken as at the 7th April) records her age as 31 yrs.
The point is that these little blips creep into records just to set us back.
There is no other candidate for a Mary Taylor dying in 1868 in GRO death reg index.
I think what Alnwick RO is looking at is the right Mary, but perhaps with a wee discrepancy of maybe a day or two. But I bet the lady at Alnwick was careful not to tell you death dates of any Mary Taylor she had in her records.
Trivia Angle.
On the 1871 census, at the top as the page which holds William Taylor, there is an Andrew Railston. I think that is Mary Taylor's dad !
Michael