I can narrow the founding date for you a little - Pettigrew & Oulton's Directory of 1847 shows "Paul & Vincent, farming implement manufacturers and iron founders" at 5 & 6.
In the 1845 edition they are listed at number 4 on the same street, in 1843 without a number but between 3 and 4.. there may have been some renumbering.
There's no sign of the business under that name at Blackhall Place in the 1842 or 1840 listings, however the 1842 list shows a possibly related business on the street "Osborne & Paul" farm implement manufacturers, no sign of a business with the surname Paul or Osborne at Blackhall place in the 1840 listing.
I've checked the alphabetical index of merchants & traders so see if I can locate any listing showing Mr Vincent's first name.. but so far I've not found any seperate entry for him - the listings I've seen are under their trading name "Paul & Vincent"