"The church is in Bramshaw and is dedicated to St Peter. It's full of yews (natch) and I was half expecting to find a well in the grounds! The map ref, according to one website that mentions the church, is SU264166, for anyone interested (and, no - it's NOT marked as a barrow on the map)"
there seems to be something here - but is this well ancient or merely old?
'Hampshire Treasures: Volume 5 ( New Forest), Page 24 - Bramshaw, Entry 01
Group D - Buildings, Monuments and Engineering Works
Well
Irons. Old Healing Well, name taken from the colour of its water. Square in plan and lined with timber. Originally a pond for the gun-powder mills at Eyeworth. O.S.A. SU21 SW2.
SU 229 147'
http://dspace.dial.pipex.com/town/avenue/pd49/places/wells/hantswel.htm