Paul - I think you're going to have to get Annie and Harry's marriage certificate

That will give you her father's name and occupation, and hopefully her age, and I might then be easier to trace the family.
I can't find a Powell family with children of those names and ages in either the 1881, 1891 or 1901 censuses.
I can't either find birth registrations in Chester district for those names at those years
Unless you have additional information, then I think the marriage certificate will be recessary to progress this line

How certain are you of the names and dates of birth ?