Don,t think this is directly connected to the above but wonder if any of the following rings a bell. My family flitted back and forth to westmorland over the years.
William Hayes to Wm and Mary 1803 Cheltenham Nothing else.
William marries Mary Camm,of Lancaster, Kendal 1832
Thomas Hay born to above Kendal 1833.
Jane born 1839 Warrington.(also, variously, Richard, Charles and James)
William died in Lancaster.
Thomas was a gardener/ nurseryman in Kendal for yonks, died there in 1906.
William was a gardener. Could be a connection with the Hayes garden centre, but can,t follow that through.
If any of the above rings a bell, or anyone can make a connection between Cheltenham/ Kendal/ Lancaster, it would be good news. Another slightly interesting point is that William gave himself a middle name , Arkley (soundex). Not a family name as far as I know.
Happy days