I personally discount other people's family trees when going this far back and instead work solely on primary sources. Incorrect information is copied from tree to tree over and over again until it becomes so muddled that it actually becomes detrimental to the family historian, rather than beneficial.
As Vance Mead has already mentioned, the social class of the family will basically determine how possible it is to research further back. At this point, you are relying on the family having had assets, in the hope that they distributed them via wills and were included in local land records etc. Unfortunately, a lot of documents this old have been lost to time as well

Are you descended from this couple? If so, you presumably have a baptism record for at least 1 of their children or some more evidence than you have included to suggest descent?
There is a burial for an Anna Fletcher, wife of William, on 13th August 1606 in Lenton, and then a month later a burial for a William Fletcher on 13th September. Unfortunately, I can only view a transcript so not sure if there is extra information.
See page 5 of this:
http://hausegenealogy.com/source/Article_Finney.pdfAnd included within is a transcription of the will of Anna's mother, which mentions Anna's children by William (Henry, Alice, Margery and Anne Fletcher). I can not view this will myself, but I see no reason it should not be an accurate representation of the document.
Interestingly, Anna's mother also died in August of 1606, with her will being written only days before the burial of her daughter, so I am wondering if there was some sort of deadly illness going round.
Queenie
