I checked the freeBMD site again, however, Births do not include parents' names and Marriages don't include spouses. As well, I tried to cross-reference Vol. nos. in marriages, but came up short. (Only 2 of the children were born in the UK, so matching up siblings was not practical).
I guess I'll have to finally give in and pay for some searches on 1837.online; but might prove costly when I don't know which area I'm looking for.
Perhaps when Ancestry distributes the 1841 online, I'll have some luck, although my understanding is that the 1841 does not provide much info (ie relationships)?
Frustration lies in the fact that David Richardson was a rather prominent newspaper owner/publisher/editor of the Galveston Daily News, which lasted from his entry into the States in 1848 until his death in New York in 1871. ALL my searches with the appropriate US agencies, & including the newspaper itself, has produced nothing. I even purchased a book which includes several entries referencing David, but NO date/place of birth anywhere! The closest I've come is the Handbook of Texas online which gave me my original info (ie birth "about 1815-19 England". Oh well......
Again, my thanks David - much appreciated.