One thing that is fascinating to me are the painted equivalents of billboards. These survive (not always intact) for decades and probably centuries in some cases (in Stamford we have "Loose boxes and stabling" on what form recollection is now a hardware store).
I would add water troughs to the list.
I will also add that while I was visiting South Mimms graveyard (in the village, not the service station) many years ago, I happened across a gentleman recording the details of the graves, of which (other than the organization for which he was volunteering) there was no central record.
Foundation stones can be interesting, and dated architectural features, and of course unusual manhole covers (I believe there used to be a coterie of folk who made rubbings of these) though they are not exactly monuments.
On war memorials note that not all are traditional stone crosses. The organ at St Paul's, Winchmore Hill is a war memorial, and Stamford has a wooden one outside All Saints, in addition to the rather grand affair near Browne's Hospital (and a third inside St Mary's).