This is pure speculation but there was a WALDRON family living in Bow at that time - John and Elizabeth WALDRON aged 30 living in Bow 1841 Census with children John, 4 and Elizabeth 1
By the 1851 Census Elizabeth WALDRON has two more children living in Bow with her: Mary 8 and 2, as well as Elizabeth now 14. John is presumably away (see below).
In 1851 there is a William WALDRON aged 22 a servant around the corner in Zeal Monachorum with a birth place of Zeal Monachorum, possibly your man.
A John WALDRON of Clannaborough married Elizabeth HEARD in Bow in 1836.
The John WALDRON from the above censuses seems to have moved to Bermondsey in London (as did a large number of people from around Bow employed in the Tanning trade in the mid 19th century).
I think the residence of your William WALDRON at the time of his marriage to Ann HOWARD reads as Broad Nymet, a tiny parish now incorporated with Bow.
It is possible, as Judith suggests, that your William was born out of wedlock. I found one William baptised in 1833 in Zeal Monachorum to a single mother, Joanna GIBBINGS.
Good luck with your research!
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