Hi David
I don't claim to be much of an expert on this subject, but here are a couple of thoughts just to get the ball rolling.
Firstly of course the Royal Arsenal at Woolwich had its own foundry and boring machinery for the manufacture of cannon.
But there were several, probably many, private firms manufacturing cannon as well. The names that come instantly to mind are
John Wilkinson at Bilston in the Black Country, the
Carron Works nr. Falkirk in Scotland and
Walkers in Rotherham. Regarding the latter there was a thread on here some while back. Hopefully this link will get you there.
http://www.nelsonandhisworld.co.uk/forum/viewtopic.php?f=1&t=873&hilit=cannon What is very frustrating is that I have just a few pages here that I photocopied from a book called Gunfounding & Gunfounders (from earliest times to 1850) by AN Kennard. 1986I believe. The pages I copied were just about the manufacturing process but I imagine the rest of the book could have lots of information about the manufacturers themselves. I think the full book has 172 pages. There are second hand copies on the web for approx £32 upwards or you could most likely order a copy through your local library.
Hope that's of interest just for starters.
MB