Dear Chris,
I just happened to stumble across this website when I was looking up a cousin on the internet. I am from the Beardsmore branch that went to New Zealand. Having emigrated when I was 10 I don't know much about the family history but my parents are still alive and my father is Frank Beardsmore. His mother was Florence Anne who married I think Joseph Beardsmore. My dad still has a brother and two sisters alive in England, my uncle Alan would probably be the best source of information but you may already have made contact with him. I do have a copy of a family tree with many of the names that have been mentioned in other posts. I know you posted the question in 2005 so it is probably old news by now.
Cheers
Sue McKee