The Bramshaw register transcript shows the following children:
George Dibden/Fleet, bapt 28 Feb 1813, parents William Dibden & Lucy Fleet, baseborn
Eliza Dibden/Fleet b 20 Nov bap 18 Dec 1814, parents William Dibden & Lucy Fleet, baseborn, buried 7 Jun 1829 aged 14 (as Fleet)
Ann Fleet, baptised 14 Jul 1816, parents William Dibden & Lucy Fleet ? buried 15 Sep 1833 age 17 as Dibden
Harriet Fleet, bapt 17 Aug 1818, parents William & Lucy Fleet, ? buried 23 Feb 1829 aged 10
William Fleet, bapt 30 Apr 1820, mother Lucy
Lucy Fleet, bapt 17 Mar 1822, mother Lucy
Joseph Fleet, bapt 8 Jun 1824, mother Lucy
Maria Fleet, bapt 17 Jan 1827, mother Lucy, buried 6 Feb 1833 aged 6
Louisa Dibden/Fleet bapt 31 Aug 1828, parents William Dibden & Lucy Fleet, baseborn
I also found the following, but according to the 1841 census, they belong to a different William and Lucy, and are in Eling in 1841:
Mark Dibden bapt 24 Feb 1835, parents William & Lucy
Andrew Arthur Dibden bapt 8 Mar 1835, parents William & Lucy
William Dibden, bapt 9 Jan 1837, parents William and Lucy ? buried 12 Feb 1837, infant
I can't find anything for Lucy Fleet, but there are a couple of possibles for William:
William Dibden bapt 25 Dec 1786 Sherfield English, father John.
William Dibbden bapt 25 Oct 1789 in Bramshaw, parents Joseph & Christian.
The father's name of Joseph and the appearance of Joseph as one of the children's names may be a clue.
Given the proximity to Wiltshire, you need to look there too. No sign of a marriage for William & Lucy.
Do you have any of the family on the 1841 census?
Nell