Rick, I wrote an article on corkcutting for the Jan 2004 issue of Family History Monthly - Issue 100. You can get back issues from the magazine. This would give you lots of background information.
The name Avern crops up a lot with corkcutting and as both the name and the trade are not very common, I feel this is more than coincidence. The Minories was the recognised centre for corkcutting firms in London but before that address, there were Averns corkcutting at 75 Oakley St.Lambeth. There is a Sun Life Fire Office record of them there in 1817, and they are still there in the London 1851 Post Office directory.
There is also a James Avern running a corkcutters in Southampton at 12 West St. in 1859.
Earlier still in Chester, there is a Joseph Avern applying for his city freedom in 1706 and a Thomas Avern being given as the corkcutter master on various apprenticeship indentures from 1810 - 1818.
I have a few photos of the Silves factory at work but my computer is not good at sending readable pictures. Can I get them to you by ordinary mail?