Hello all - I read Goldcoast's post very early this morning, and the Cooley/Cork mystery has been revolving in my head ever since.
Thank you so much, Casalguidi, for pointing the direction to the older research, although I wouldn't want to put Goldcoast off at the start!!
I am mailing Royd (of this forum) who also has Cork connections in the Chatham area at the time - irritatingly, some of the facts you mention are ringing a vague bell in my mind (but don't place any weight on this, yet), and I want to see if anything connects with Royd's family.
In very brief summary, Goldcoast, of mine and Royd's Cork(e)/Cooley connections:
It appears that a Richard Cork(e), born in 1817 in Stone, Kent, who was an itinerant farm labourer, had a family with a Jane Cooley (born c 1820 in Surrey), and they moved through Kent and Surrey borders, as "travellers".
We can follow them because of the baptism records of their children, as well as some censuses. There's no marriage record for Richard and Jane, and their children variously called themselves Cork or Cooley.
My great great grandfather, another Richard Cork (Richard and Jane's son), did marry my great great grandmother, and their daughter was registered as Cork. However, the two split up, and the very long thread Casalguidi mentions, finds that Richard moves to Chatham and marries (bigamously), using his mother's name, Cooley.
As I mention in this thread, his first two children with the new "wife" ahead of their bigamous marriage, were registered as Cork, but then the whole family changed their names and became Cooley.
So I will have a good look round again, and see if I can link in Bertha - the very mention of the address in Chatham, the names both Cork and Cooley, and the working in a shipyard, whether Kent or Scotland, seem to suggest irresistibly that there is some connection somewhere!
Back to you, later, and will alert Royd also.