I can find no firms around that date that fit, nor any firm jordan in milk St (though a very small firm might not be in the directory). However I have found the following in local directories at a later date:
1869-68 Jordan & Greaves, leather legging manufrs. 96 Granville st
1872 Jordan & Dawson, leather legging manufrs. 96 Granville st
1873 Jordan & Dawson, boot upper manufacturers, 93-96 Granville st
1876 James Jordan, James, legging manufacturer, 93-96 Granville st
1878-82 Jordan, James, legging manufacturer ,Exeter st
1883 Jordan, James & Co. Boot leather upper manufacturers, Bread St
1884 Jordan & Co. boot upper & leather goods manufs. Bread st
1888 Walker Thos. leather goods manufr. Bread st
1890 Walker, Thomas, Leather goods manufacturer, Bread St
The factories in 1884 & 1888 are at the same position in Bread St, though no number is given, I am sure they are the same factory
Before 1888 there are a number of Thomas Walkers, none very closely associated with leather. The nearest is a belt & braces manufacturer , 3 Brook St, St Pauls