Thanks JenB, we have checked freebmd first and then familysearch to try to narrow it down. But we can't. Don't know if we are confused or not, as we are working on the fact that Robert was born in 1823 and Jane in 1833? Many thanks
Robert is on the 1881 census, but Jane is a widow by the time of the 1891 census.
In 1881 they are living in Kimbleworth, which was in Durham Registration District. In 1891 Jane is still living in Kimblesworth, so the likelihood is that Robert died there.
So you must search freeBMD for a death of Robert Atkinson, between 1881 and 1891, probably in Durham Registration District.
There is only one possible candidate that I can see - Robert Atkinson who died in the 3rd quarter of 1889, aged 66, i.e. born, as you have said, in 1823.