It seems to me that there were a number of couples with the names Daniel & Elizabeth Kirk. I have found another one born in 1807 who was a gardener too!
I suspect that this may be Daniel's son, ie Jane & Sarah's brother. There is a marriage 23 May 1825 at Nottingham St Mary that would fit - Daniel Kirk & Elizabeth Atkinson.
Baptised at the same church:
16 Apr 1826 Harriet d/o Daniel & Elizabeth Kirk of Octagon Row
16 Dec 1828 Eliza d/o Daniel & Elizabeth Kirk of Sherwin St
29 Dec 1829 Eliza d/o Daniel & Elizabeth Kirk of Sherwood St
14 Feb 1831 Elizabeth d/o Daniel & Elizabeth Kirk of Sherwood St
15 Aug 1832 Sarah Ann d/o Daniel & Elizabeth Kirk of Mansfield Rd
In 1841 Daniel is with daughters Eliza, Elizabeth, Sarah & Hannah (c1837) in Bramcote, and the 1851 census you posted states that Emma Kirk was born in Bramcote in 1841, so the family certainly fits. This Daniel says he was born Loughborough, and as the baptisms in Basford were of adults, with two making reference to Loughborough, I'd say its a strong possibility.
The baptism of Hannah Kirk on 14 Feb 1836 at St Leodegarius, Basford, is therefore quite possibly the Hannah in Bramcote on the 1841 census.
Also from my CD of Prison Calenders, although Im not sure where he fits in, if at all:
8 Jan 1855, Thomas Kirk, 39, Gardener, of Loughborough, charged with theft.