Hi. I have come to this Elizabeth Gaudern and John Linnell discussion rather late, but I have this to add:
I was researching William Gaudern who was the Administrator for the affairs of an ancestor (his sister I think) in 1851, and I discovered him living with his wife Alice and unmarried daughter Harriet (born 1808) in South Kilworth, in the census of 1851. I looked for them again in 1861 (by which time I guess William and Alice were dead, though there's no death certificates to be found - goodness me these Gauderns are indeed elusive) and there was the same Harriet 10 years older, still unmarried and living with a farmer called John Linnell and his wife Elizabeth in Sulby. It is a fair guess that Elizabeth was Harriet's married sister and I am therefore able to tell you who Elizabeth Linnell's Gaudern grandparents were.
They were Stephen Gaudern married to Frances Weldon (1739 - after 1813) of Duddington. I can only be certain of this from family wills because the Gauderns seem to be allergic to all records. I had not known they had a son called William until I looked in the wills and probate section of Find My Past, but they did have a son called James, and a James William Gaudern died in the Oundle district in 1862. This last bit is only a guess, but it is definite that William Gaudern of South Kilworth was a very close relative of Frances Weldon (nee Gaudern), who was definitely a daughter of Stephen and Frances Gaudern (nee Weldon). If you are muddled it is because the Weldons were dead keen on marrying their first cousins.
Hope this helps