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There is solid evidence for John being the son of William Henley and Ann White. Ann came from St Clement Danes, Westminster. In 1803 (information from the Russelll archives) she was a housemaid in Woburn Abbey alongside Catherine Henley, William's cousin, and her elder sister Lettice was a witness at John Henley's own marriage in Brighton in 1838. The mystery was William Ralph. Looking at the dates of birth he cannot have had the same mother as John. William Ralph was the illegitimate son of Anne Ralph, who never married. His father was a William Henley: most likely the same one, though could have been his uncle. Too many Williams! The big question is who were the parents of Joseph born 1799. My best guess is William Henley and Mary Raklph, both then aged 17. Mary Ralph was Ann's sister. There was another child, in 1802, christened 23 May: Rebecca Ralph (father unnamed, mother Ann Ralph). Rebecca died 5 Aug 1802. Complicated story. And that's before we try to unravel the White family in Woburn and in St Clement Danes. That one is not for rootschat because I doubt if there's any documentary evidence that would help - but it seems that William White (Ann's and Lettice's father) had a family in Woburn 1750s to 1770, and another family in St Clement Danes 1772-1785. He was the tenant and ratepayer of 14 Leighton Street, Woburn until his death in 1810, when the tenancy was taken over by Andrew Henley (William's father). 

I have the typewritten copy but need confirmation from original parish registers or bishop's transcripts because there are three baptism entries that don't make a lot of sense.

Joseph born 23/12/1799 bapt 23/2/1800 William and Mary Henley. There were no William and Mary Henley marriages in Woburn. Could it have been William Henley and Mary X or William X and Mary Henley, or could the 'Mary' be incorrect, as William Henley and Sarah would make sense? This Joseph doesn't seem to appear anywhere in subsequent records so possibly the William and Mary are from elsewhere, not otherwise appearing in Woburn parish records.

John born 16/11/1810 bapt 9/12/1810 William and Ann Henley
William Ralph born 16/4/1811 bapt 30/6/1811 William and Ann Henley
This is of course impossible if it's the same Ann. I think John is definitely the son of William Henley and his wife Ann (nee White). I think Ralph is the surname of the other Ann - who was unmarried and 5 years older than William (if it was the same William Henley). So that the child was given the surname Ralph, not a middle name Ralph.

Are there any clues in the original handwritten registers?

I have now received a much better resolution copy from TNA (full marks to them for recognising and fixing the problem!). No longer a resolution issue. Just deciphering some very bad handwriting. What I get from this so far is

Superintending the Dismantling the *****ian* Ships from 8 Nov 1808.

Just one word to decipher. Presumably they were dismantling captured ships that were too badly damaged to be of any value. Could be Austrian, except I can't find a capital A and I didn't know there would have been any Austrian ships to dismantle.

Many thanks for these erudite replies! I knew I could rely on Rootschat for expert answers to obscure questions! In fact different members of this same family did sail fairly close to the wind - with at least three first cousin marriages in 19th and early 20th century that I know about. Fortunately there were none of the descendants of those marriages who themselves intermarried!

More practically, if the marriage to Harriet's sister Miriam was automatically considered null and void, then I presumably would be wasting my time searching for any annulment documentation. What is really sad is that she outlived the man she believed to be her husband by over 20 years, continued to use his surname, and identified herself as a widow in the 1911 census.