Many thanks for the replies. Because of the scope of this forum I had intentionally kept my question fairly general and focussed on the wording in the will, but maybe a bit of background would be helpful.
It is over 20 years since I first researched this illegitimate family (their surname was Pritchard). There were 6 children baptised between 1801 and 1809 in a small Wiltshire village; none of the children had middle names or other names which pointed to their father's identity. I did all the usual searches in bastardy and poor relief records to no avail, and without going into lengthy details, eventually came to the conclusion that most likely the father was a man of means and that he and the mother were living together. (She had been married but no longer with her husband.) I even drew up a list of suspects and checked all available wills of those on the list.
Scroll forward 20+ years, and the arrival of Wiltshire parish registers at Ancestry inspired me to look again at this family, and to cut a very long story short, my further investigations led me to look at the will mentioned above (the testator was a Thomas Comley), which was biggest clue to date as to the paternity of the children.
Since posting the above, I have found another supporting clue. One of the illegitimate sons married as a minor by licence, and I viewed this as part of my initial research. What didn't show up in the archives catalogue 20 years ago, but does now in a more recently compiled index, is that a couple of weeks before the marriage licence was granted, he had a licence application refused, and the index entry for this failed application indicates that he named his father as Thomas Comley. I now need to request copies of this to see the full details, though of course, being named as the father doesn't prove he actually was.
Which takes me back to the wording of the will - I believe that 'cohabiting' would normally have indicated living together as if married, but I was a bit thrown by the 'as my housekeeper' bit.