You girls are absolutely brilliant. A quick synopsis of the information you have gathered for me:
1841 Census Morgage Row, Newick.
James Budgin 40
Sarah Budgin 40
Christian Budgin 7
James Budgin 5.
1851 Census Rough, Newick.
Sarah Budgen 56, Widow.
Jane Budgen 27
James Budgen 15.
75 West Street, Brighton
Thomas Bryer 46
Mary Bryer 50
Christina Budgen 19
William Greaves 18
1853 Death Newick
Christiana Greves (Age unknown)
1861 Census Chailey
Sarah Budgen 64 Widow
William Greaves 8 grandson.
There are quite some possibilities here. The ages for 1841 were rounded down so it would seem there is a strong likelihood that Sarah is the same in the three census returns, although there is a 2 year discrepancy in the middle.
Christian could conceivably be Christina and Christiana, allowing for the poor literacy standard of the time. Similarly the changing of the name from Budgin to Budgen could be a spelling error.
Having a Christina Budgen and William Greaves residing at the same residence seems a very big coincidence. The death of Christiana Greves in 1853 also adds weight to William aged 8 living with his grandmother, with his DOB approximately 1852. Unfortunately the entry on FreeBDM does not give an age at death.
I know I am seeing things here that have not yet been proved but hopefully with a little more digging, I will be able to say yea or nay.
Once again thank you for your efforts, this site has amazing people as members, and nothing seems to be a problem to assist other searchers.
Possibly another visit to the local LDS centre is in order to search their records.
Cheers from Australia.
Gordon.