Some good thinking here so far: thank you. In reply:
Yes, it all happened in East Malling; my wife was born nearby in Basted: there were (and are) a lot of Woodgers in the area.
Elizabeth was christened in February 1793 and the banns were read in March 1814, so she had just passed her 21st birthday.
She and Edward Wooding had further children, after their wedding, who were christened Wooding (not Woodger)
The name was variously spelled Woodyer, Woodgier, Woodger; it has settled down as Woodger since those far off days 200+ years ago
Edward jnr remained Woodger in the censuses till his final one (1881).
Elizabeth would have been 19 when she conceived Edward; I am not aware of any previous 'spurious' children
I cannot see any reference to his or his bride's parents on the banns and wedding records - which on all fam hist sites are only transcripts. On both of these he appears as Edward Wogger (no worse than one elusive Thomas Proctor, who appears as Thomas Prodger in one census).
I guess the only way to explore further whether his biological father was Edward Wooding would be to compare Wooding and Woodger DNA as the forum kindly explained at great length for me on another thread: but as it is my wife's family, I shall leave that to her after she retires and develops the hobby more. Once again, many thanks.