Just found image of that marriage record and William's signature is quite similar to his signature a few years earlier when he and his brother John were witnesses to his mother's second marriage. he had to squeeze it in the space as Mary signed first with such a large signature it overflowed on the line below.
They had a son William Noah Street baptised in 1776. I am wondering if that was the William who married Little Dixon.
In 1841 his birth year calculates as 1776, if it was 1779 it should be rounded to 1781. Little's age is rounded to 1781. In 1851 his age is given as 72, same as Little's, co calculated birth year is 1776. But looking in the disability column he is blind, so wouldn't be able to fill in householder's form himself, so Little or whoever filled it in just guessed at his age. His age at death would give birth year of 1778, but as he died in Q1 of 1860, he may not have had his birthday in that year yet. William Noah Street baptised in May 1776. Little died in 1859, so could not have been the informant.
The record of marriage for William Street and Mary Groome says she was from Arundel. Warningcamp is quite near Arundel as well.
The Lyminster William could be an adult baptism, I have often seen those recorded without parents, and that William is just a co-incidence and not related.
I think brother John may have died a bit later than I said, I've found another burial in 1828 which is a good fit on age and place.