Derek I'm not at the moment going to be any help with your hunt for Ann. There are none in my family line but I've not yet explored all the various uncles and aunts so she could be in there, the area is right.
The answer to your...are you related to Gregory of Youlgreave? is - I believe so. Thomas Gregory married Hannah (u/k surname) at Bakewell in Oct. 1752. First recorded child, Richard, born 1754. Third recorded child William, born 1759. Hannah died in 1783. Thomas died in 1795. Thomas remarried, who, where, when U/K. His Will says "...my loving wife.." Will written March 1795. Thomas, Hannah, three infant children and adult son Samuel.
William is a "beneficiary" in Thomas's Will, he got ONE shilling, as did two others. William Gregory married Sarah(U/K), where and when also unknown. William and Sarah's first child born 1786. Their sixth and last child, John, was born in 1796. John went on to marry Elizabeth Titterton and they are my GG Grandparents.
I believe Thomas is this William's father because of the following four connections:
1.) 1780 Tax record for Wheeldon Trees Farm, Hartington Middle Quarter, paid by Thomas Gregory. 1786 Tax record for ditto, paid by William Gregory. 2.) William and Sarah's second child, Peter, died aged seven in 1796. Peter is buried at Great Longstone. Parish register entry reads " of Wheeldon Trees ". 3.) Great Longstone Parish Register records on 11 March 1806 burial of "William Gregory of Hartington" (Meaning Hartington Middle Quarter) 4.) William and Sarah's fourth child, Samuel, died aged 29 years in 1822. The Great Longstone Parish Register entry states " Samuel Gregory, son of William, age 30, late of Wheeldon, Crowdecote"
My brick wall is to nail down Thomas's parents, I have suspects but I can't get any firm evidence at the moment. Then, I want to find out about Thomas's second wife, can't find anything at all on that.