Directory of Liverpool in the year 1824.
It lists residents and traders, but not necessarily the whole population and gives details on the area, together with a social history. These type of publications don't just list the elite this is a common misconception. There are plenty of people of average standing in the community, such as Butchers, Joiners, Shopkeepers, Boot & Shoe Makers etc
However even if you know for certain that a relative was living in a particular place at a certain time it does not automactically follow that you will find them in a book as it was the individuals choice as to whether they went into these type of publications, but it's great fun looking & you might get lucky !