Some mentions in the papers:
Report of a meeting of the Health Committee (Liverpool Mercury 11 February 1863 ):
" A letter from Mr John Atkinson ....was read,. It complained of injury which his property at the corner of Hurst Street and Carpenter's Row had sustained ...."
John Atkinson, Hurst Street, on the committee for the Licensed Victuallers Charity Ball in 1855 (LM January 16 1855)
A letter from John Atkinson 33 Hurst Street, concerning implications of the Sunday Beer Bill (LM 28 August 1855)
Death notice (LM 27 November 1858):
"Nov.19 aged 76 Elizabeth wife of Mr T Atkinson of Penrith, Cumberland, and mother of Mr John Atkinson, licensed victualler, Hurst Street, this town"
There are probably lots more newspaper mentions to find but that's all I have time for this morning !