Sorry, Fishergate, no Beattie or Ferguson listed among the Tea Dealers, or Grocers in the 1824 Liverpool directory.
In the alphabetical list there's a Jane Beattie who kept a boarding house at 18 Standish Street, and five Fergusons - Alexander who kept a pub, the Edinburgh Castle; James A. who kept the Union Tavern; Thomas, a joiner; and two Williams, a mariner and a hairdresser.
Also had a look at Manchester, but no joy there either.