First - I am certain that my Henry's father was James. I have Henry's marriage certificate and his father's name is given as James.
Next, I recently came across someone on another website interested in the family, who gave me the name Ann Harris, and a number of Henry's siblings - James included. A lot of other information she gave me was consistent with data I had already collected - particularly baptism and burial records from Albury parish. I got these from the Surrey History Centre in Woking - but a lot of them are now published on http://www.alburychurches.org/history/christeningsa.html (you have to look for both Atfield and Adfield)

Unfortunately, the baptism records on the website do not include the names of parents, but those at Woking do. At the time, I did not go back far enough to pick up Henry or James baptism record - so cannot confirm that their parents are listed as James and Ann in each case. But all the other data I was given by the lady on the other website tallies more or less exactly. So I am very confident that the bit about James and Ann is correct.
What do you think?