I have occasionally found mistakes at Yorkshire Burials, but they have a facility for reporting them and so long as they agree, are very quick to correct them. However, in this case I think there are two Annie Smiths, so the question arises whether this is actually the right burial and grave.
Because of the number of people buried in the same grave at more or less the same time, I'm inclined to think the Harehills date is correct for that particular Annie. Note the age is given as 89, and FreeBMD has a death for an Annie E Smith in the Lower Agbrigg district in the March quarter of 1954, age 89, which fits nicely.
That means the Annie who died on 2 July 1954 must be buried somewhere else - so if you're sure that's your ancestor (and your reply #2 suggests you are), we must look for another burial. I can't do it myself just now, but do have a good search at Yorkshire Burials - I don't think they claim to have 100% coverage, but it's the best place to look for a burial in the Leeds area.
And in case anyone else wants to have a search, what was your Annie's age given as on the death certificate, what was her usual address, and where did she die?
